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Mathematical methods to study the polling systems. (English. Russian original) Zbl 1126.60321
Autom. Remote Control 67, No. 2, 173-220 (2006); translation from Avtom. Telemekh. 2006, No. 2, 3-56 (2006).
Summary: Reviewed were the mathematical methods that are used to investigate the polling systems which found wide application in modeling and design of various transport and industrial processes. Emphasis was made on the models of polling systems used to investigate the wireless broadband networks. The polling systems were classified; presented were stochastic models and methods of investigating discrete-time and continuous-time systems, systems with cyclic, periodic, and random queue polling, as well as the methods of their optimization.

MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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[1] Al’bores, F.Kh. and Bocharov, P.P., Analysis of Two Limited Relative-priority Queues in the One-server Queuing System with Phase-type Distribution, Avtom. Telemekh., 1993, no. 4, pp. 96–107.
[2] Bakanov, A.S., Vishnevskii, V.M., and Lyakhov, A.I., A Method for Evaluating Performance of Wireless Communication Networks with Centralized Control, Avtom. Telemekh., 2000, no. 4, pp. 97–105.
[3] Vishnevskii, V.M., Wireless Networks for Broadband Access to the Internet Resources, Elektrosvyaz’, 2000, no. 10. pp. 9–13.
[4] Vishnevskii, V.M., Teoreticheskie osnovy proektirovaniya komp’yuternykh setei (Theoretical Fundamentals of Computer Network Design), Moscow: Tekhnosfera, 2003.
[5] Vishnevskii, V.M., Lyakhov, A.I., and Guzakov, N.N., Estimation of the Maximum Throughput of the Wireless Access to Internet, Avtom. Telemekh., 2004, no. 9, pp. 52–70.
[6] Vishnevskii, V.M., Lyakhov, A.I., Portnoi, S.L., and Shakhnovich, I.V., Shirokopolosnye besprovodnye seti peredachi informatsii (Broadband Wireless Information Transmission Networks), Moscow: Tekhnosfera, 2005.
[7] Gavrilov, A.F. and Krasil’nikov, Yu.P., Cyclic Service with Direct Information Connection, Avtom. Telemekh., 1976, no. 10, pp. 17–22.
[8] Efrosinin, D.V. and Rykov, V.V., Numerical Study of the Optimal Control of a System with Heterogeneous Servers, Avtom. Telemekh., 2003, no. 2, pp. 143–151. · Zbl 1071.60086
[9] Zhdanov, V.S. and Saksonov, E.A., Existence Conditions for Stable Modes in Cyclic Queuing Systems, Avtom. Telemekh., 1979, no. 2, pp. 29–38. · Zbl 0418.93047
[10] Kitaev, M.Yu. and Rykov, V.V., Queuing System with Branching Flows of Secondary Customers, Avtom. Telemekh., 1980, no. 9, pp. 52–61.
[11] Kovalevskii, A.P., Positive Recurrence and Optimization of Polling Systems with Multiple Servers, in Aktual’nye problemy sovremennoi matematiki, Novosibirsk: NII MIOO NGU, 1997, vol. 3, pp. 75–86.
[12] Klimov, G.P. and Mishkoi, G.K., Prioritetnye sistemy obsluzhivaniya s orientatsiei (Priority Queuing Systems with Orientation), Moscow: Mosk. Gos. Univ., 1979.
[13] Lakontsev, D.V. and Semenova, O.V., Mathematical Models of Centralized Control in Wireless Networks IEEE 802.11, in Raspredelennye komp’yuternye i telekommunikatsionnye seti (DCCN-2005) (Distributed Computer and Telecommunication Networks (DCCN-2005)), Moscow: Tekhnosfera, 2005, pp. 77–83.
[14] Nazarov, A.A. and Urazbaeva, S.U., Study of the Decomposed Model of the Multi-Packet Mode of Communication Network with DQDB Protocol, Vest. Tomsk. Gos. Univ., Matematika. Kibernetika. Informatika, 2002, no. 275, pp. 199–201.
[15] Nazarov, A.A. and Urazbaeva, S.U., Study of Discrete-Time Queuing Systems and Their Application to Analysis of Fiber-Optic Communication Networks, Avtom. Telemekh., 2002, no. 12, pp. 59–70. · Zbl 1116.90331
[16] Rykov, V.V., On the Monotonicity Conditions for the Optimal Control Policies for Queuing Systems, Avtom. Telemekh., 1999, no. 9, pp. 92–106.
[17] Rykov, V.V. and Verbitskii, S.N., Analysis of Some Algorithms for Polling Web-pages, Vest. Ross. Univ. Druzhby Narodov, Prikladn. Mat. Inform., 2000, no. 1, pp. 96–104.
[18] Saksonov, E.A., Study of Multi-Channel Closed Cyclic Queuing System, Avtom. Telemekh., 1979, no. 12, pp. 80–86.
[19] Saksonov, E.A., A Method for Calculation of the Marginal State Probabilities of the Cyclic Queuing Systems, Avtom. Telemekh., 1997, no. 1, pp. 85–89.
[20] Timofeev, E.A., Optimization of Mean Queue Lengths in a Queuing System with Branching Flows of Secondary Customers, Avtom. Telemekh., 1995, no. 3, pp. 60–67.
[21] Titenko, I.M., On Cyclically Served Multi-Channel Systems with Losses, Avtom. Telemekh., 1984, no. 10, pp. 88–95.
[22] Foss, S.G. and Chernova, N.I., On Polling Systems with Infinite Number of Stations, Sib. Mat. Zh., 1996, vol. 37, no. 4, pp. 940–956. · Zbl 0882.60089 · doi:10.1007/BF02104674
[23] Foss, S.G. and Chernova, N.I., Comparison Theorems and Ergodic Properties of the Polling Systems, Probl. Peredachi Inf., 1996, no. 4, pp. 46–71.
[24] Yakushev, Yu.F., On Optimal Protocol of Multiple Marker-Type Access in Local Computer Network, Avtom. Telemekh., 1990, no. 10, pp. 125–134.
[25] Adan, I.J.B.F., Boxma, O.J., and Resing, J.A.C., Queuing Models with Multiple Waiting Lines, Queuing Syst., 2001, vol. 37, no. 1–3, pp. 65–98. · Zbl 0974.60079 · doi:10.1023/A:1011040100856
[26] Afanassieva, L.G., Delcoigne, F., and Fayolle, G., On Polling Systems where Servers Wait for Customers, Markov Process and Related Fields, 1997, vol. 3, no. 4, pp. 527–545. · Zbl 0911.60075
[27] Ajmone Marsan, M., Donatelli, S., and Neri, F., GSPN Models of Markovian Multiserver MultiQueue Systems, Performance Evaluat., 1990, vol. 11, no. 4, pp. 227–240. · doi:10.1016/0166-5316(90)90001-Y
[28] Almási, B., A Queuing Model for a Non-homogeneous Polling System Subject to Breakdowns, Ann. Univ. Sci. Budapest, Sect. Comp., 1999, vol. 18, pp. 11–23. · Zbl 0943.60090
[29] Altman, E., Blanc, H., Khamisy, A., and Yechiali, Y., Gated-type Polling Systems with Walking and Switch-in Times, Commun. Stat.: Stochastic Models, 1994, vol. 10, no. 4, pp. 741–763. · Zbl 0806.60093 · doi:10.1080/15326349408807320
[30] Altman, E. and Foss, S., Polling on a Graph with General Arrival and Service Time Distribution, Lett. Oper. Res., 1997, vol. 20, no. 4, pp. 187–194. · Zbl 0879.90094 · doi:10.1016/S0167-6377(97)00002-3
[31] Altman, E., Foss, S., Riehl, E., and Stidham, S., Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems, Oper. Res., 1998, vol. 46, no. 1, pp. 137–148. · Zbl 0987.90019 · doi:10.1287/opre.46.1.137
[32] Altman, E., Gaujal, B., and Hordijk, A., Optimal Open-loop Control of Vacations, Polling and Service Assignment, Queuing Syst., 2000, vol. 36, no. 4, pp. 303–325. · Zbl 0974.60077 · doi:10.1023/A:1011085302786
[33] Altman, E., Khamisy, A., and Yechiali, U., On Elevator Polling with Globally Gated Regime, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 85–90. · Zbl 0752.60071 · doi:10.1007/BF01159288
[34] Altman, E. and Kofman, D., Bounds for Performance Measures of Token Rings, IEEE/ACM Trans. Networking, 1996, vol. 4, no. 2, pp. 292–299. · doi:10.1109/90.491015
[35] Altman, E., Konstantopoulos, P., and Liu, Z., Stability, Monotonicity and Invariant Quantities in General Polling Systems, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 35–57. · Zbl 0752.60070 · doi:10.1007/BF01159286
[36] Altman, E. and Kushner, H., Control of Polling in Presence of Vacations in Heavy Traffic with Applications to Satellite and Mobile Radio Systems, SIAM J. Contr. Optimiz., 2002, vol. 41, no. 1, pp. 217–252. · Zbl 1102.90315 · doi:10.1137/S0363012999358464
[37] Altman, E. and Levy, H., Queuing in Space, Advances Appl. Prob., 1995, vol. 26, no. 4, pp. 1095–1116. · Zbl 0824.60097 · doi:10.1017/S000186780002677X
[38] Altman, E. and Spieksma, F., Polling Systems: Moment Stability of Station Times and Central Limit Theorems, Commun. Stat.: Stochastic Models, 1996, vol. 12, no. 2, pp. 307–328. · Zbl 0852.60100 · doi:10.1080/15326349608807386
[39] Altman, E. and Yechiali, U., Cyclic Bernoulli Polling, ZOR–Methods and Models Oper. Res., 1993, vol. 38, no. 1, pp. 55–76. · Zbl 0778.60066 · doi:10.1007/BF01416007
[40] Altman, E. and Yechiali, U., Polling in a Closed Network, Prob. Eng. Inf. Sci., 1994, vol. 8, pp. 327–343. · doi:10.1017/S0269964800003442
[41] Baba, Y., Analysis of Batch Arrival Cyclic Service Multiqueue Systems with Limited Service Discipline, J. Oper. Res. Soc. Japan, 1991, vol. 34, no. 1, pp. 93–104. · Zbl 0735.60096
[42] Baxter, L.A., Harche, F., and Yechiali, U., A Note on Minimizing the Variability of the Waiting Times in a Globally-gated Elevator Polling System, Naval Res. Logistics, 1997, vol. 44, no. 6, pp. 605–611. · Zbl 04540670 · doi:10.1002/(SICI)1520-6750(199709)44:6<605::AID-NAV6>3.0.CO;2-7
[43] Bertsimas, D., The Achievable Region Method in the Optimal Control of Queuing Systems: Formulations, Founds and Policies, Queuing Syst., 1995, vol. 21, no. 3–4, pp. 337–389. · Zbl 0857.60093 · doi:10.1007/BF01149167
[44] Bertsimas, D. and Mourtzinou, G., Decomposition Results for General Polling Systems and Their Applications, Queuing Syst., 1999, vol. 31, no. 3–4, pp. 295–316. · Zbl 0934.90014 · doi:10.1023/A:1019118516504
[45] Bertsimas, D. and Niño-Mora, J., Optimization of Multiclass Queuing Networks with Changeover Times via the Achievable Region Approach: I. The Single-Station Case, Math. Oper. Res., 1999, vol. 24, no. 2, pp. 331–361. · Zbl 0977.90007 · doi:10.1287/moor.24.2.331
[46] Bing, B., Wireless Local Area Networks: The New Wireless Revolution, New York: Wiley-Interscience, 2002.
[47] Birman, A., Gail, H.R., Hantler, S.L., Rosber, Z., and Sidi, M., An Optimal Service Policy for Buffer Systems, J. Association Comput. Machinery, 1995, vol. 42, no. 3, pp. 641–657. · Zbl 0885.68016 · doi:10.1145/210346.210422
[48] Bisdikian, C. and Merakos, L., Output Process from a Continuous Tokenring Local Area Network, IEEE Trans. Commun., 1992, vol. 40, no. 12, pp. 1796–1799. · doi:10.1109/26.192402
[49] Blanc, J.P.C., A Numerical Approach to Cyclic-Service Queuing Models, Queuing Syst., 1990, vol. 6, no. 2, pp. 173–188. · Zbl 0702.60091 · doi:10.1007/BF02411472
[50] Blanc, J.P.C., An Algorithmic Solution of Polling Models with Limited Service Disciplines, IEEE Trans. Commun., 1992, vol. 40, no. 7, pp. 1152–1155. · doi:10.1109/26.153357
[51] Blanc, J.P.C., Performance Evaluation of Polling Systems by Means of the Power-series Algorithm, Ann. Oper. Res., 1992, vol. 35, no. 1–4, pp. 155–186. · Zbl 0760.90039 · doi:10.1007/BF02188703
[52] Blanc, J.P.C., The Power-series Algorithm Applied to Cyclic Polling Systems, Commun. Stat.: Stochastic Models, 1991, vol. 7, no. 4, pp. 527–545. · Zbl 0749.60087 · doi:10.1080/15326349108807205
[53] Blanc, J.P.C., The Power-series Algorithm for Polling Systems with Time Limits, Prob. Eng. Inf. Sci., 1998, vol. 12, pp. 221–237. · Zbl 0936.90009 · doi:10.1017/S0269964800005167
[54] Blanc, J.P.C. and van Der Mei, R.D., Optimization of Polling Systems with Bernoulli Schedules, Performance Evaluat., 1995, vol. 22, no. 2, pp. 139–158. · Zbl 0875.68094 · doi:10.1016/0166-5316(93)E0045-7
[55] Blanc, J.P.C. and van der Mei, R.D., The Power-series Algorithm Applied to Polling Systems with a Dormant Server, in The Fundamental Role of Teletraffic in the Evolution of Telecommunication Networks, Labetoulle, J. and Roberts, J.W., Eds., Amsterdam: Elsevier, 1994, pp. 865–874.
[56] Borovkov, A., Korshunov, D., and Schassberger, R., Ergodicity of a Polling Network with an Infinite Number of Stations, Queuing Syst., 1999, vol. 32, no. 1, pp. 169–193. · Zbl 0976.60089 · doi:10.1023/A:1019139121047
[57] Borovkov, A. and Schassberger, R., Ergodicity of a Polling Network, Stochastic Proc. Appl., 1994, vol. 50, no. 2, pp. 253–262. · Zbl 0802.60084 · doi:10.1016/0304-4149(94)90122-8
[58] Borst, S.C., Polling Systems, Amsterdam: Stichting Mathematisch Centrum, 1996. · Zbl 0932.90007
[59] Borst, S.C., Polling Systems with Multiple Coupled Servers, Queuing Syst., 1995, vol. 20, no. 3–4, pp. 369–394. · Zbl 0847.90058 · doi:10.1007/BF01245325
[60] Borst, S.C. and Boxma, O.J., Polling Models with and without Switchover Times, Oper. Res., 1997, vol. 47, pp. 536–543. · Zbl 0887.90072 · doi:10.1287/opre.45.4.536
[61] Borst, S.C., Boxma, O.J., Harink, J.H.A., and Huitema, G.B., Optimization of Fixed-time Polling Schemes, Telecommun. Syst., 1994, vol. 3, pp. 31–59. · doi:10.1007/BF02110043
[62] Borst, S.C., Boxma, O., and Levy, H., The Use of Service Limits for Efficient Operation of Multi-Station Single-medium Communication Systems, IEEE/ACM Trans. Networking, 1995, vol. 3, no. 5, pp. 602–612. · doi:10.1109/90.469947
[63] Borst, S.C. and van der Mei, R.D., Waiting Time Approximations for Multiple-server Polling Systems, Performance Evaluat., 1998, vol. 31, no. 3–4, pp. 163–182. · doi:10.1016/S0166-5316(96)00063-6
[64] Boxma, O.J., Models of Two Queues: A Few New Views, in Teletraffic Analysis and Computer Performance Evaluation, Boxma, O.J., Cohen, J.W., and Tijms, H., Eds., Amsterdam: Elsevier, 1986, pp. 75–98.
[65] Boxma, O.J., Static Optimization of Queuing Systems, in Recent Trends in Optimization Theory and Applications, Agarwal, R.P., Ed., Singapore: World Scientific, 1995, pp. 1–16. · Zbl 0874.90092
[66] Boxma, O.J., Deng, Q., and Resing, J.A.C., Polling Systems with Regularly Varying Service and/or Switchover Times, Advances Performance Anal., 2000, vol. 3, pp. 71–107.
[67] Boxma, O.J. and Down, D.G., Dynamic Server Assignment in a Two-queue Model, Eur. J. Oper. Res., 1997, vol. 103, pp. 595–609. · Zbl 0921.90075 · doi:10.1016/S0377-2217(97)82089-9
[68] Boxma, O.J. and Groenendijk, W.P., Pseudo Conservation Laws in Cyclic-service Systems, J. Appl. Prob., 1987, vol. 24, pp. 949–964. · Zbl 0639.60087 · doi:10.1017/S002190020011681X
[69] Boxma, O.J., Groenendijk, W.P., and Weststrate, J.A., A Pseudoconservation Law for Service Systems with a Polling Table, IEEE Trans. Commun., 1990, vol. 38, no. 10, pp. 1865–1870. · doi:10.1109/26.61458
[70] Boxma, O.J. and Kelbert, M., Stochastic Bounds for a Polling System, Ann. Oper. Res., 1994, vol. 48, no. 1–4, pp. 295–310. · Zbl 0787.60117 · doi:10.1007/BF02024662
[71] Boxma, O.J., Koole, G.M., and Mitrani, I., Polling Models with Threshold Switching, in Quantitative Methods in Parallel Systems, New York: Springer-Verlag, 1995, pp. 129–140. · Zbl 0845.68010
[72] Boxma, O.J., Levy, H., and Weststrate, J.A., Efficient Visit Frequencies for Polling Tables: Minimization of Waiting Cost, Queuing Syst., 1991, vol. 9, no. 1–2, pp. 133–162. · Zbl 0738.68008 · doi:10.1007/BF01158795
[73] Boxma, O.J., Levy, H., and Weststrate, J.A., Efficient Visit Orders for Polling Systems, Performance Evaluat., 1993, vol. 18, no. 2, pp. 103–123. · Zbl 0781.68030 · doi:10.1016/0166-5316(93)90031-O
[74] Boxma, O.J., Levy, H., and Yechiali, U., Cyclic Reservation Schemes for Efficient Operation of Multiplequeue Single-server Systems, Ann. Oper. Res., 1992, vol. 35, no. 1–4, pp. 187–208. · Zbl 0755.60076 · doi:10.1007/BF02188704
[75] Boxma, O.J. and Meister, B., Waiting-time Approximations for Cyclic-Service Systems with Switchover Times, Performance Evaluat., 1987, vol. 7, pp. 299–308. · doi:10.1016/0166-5316(87)90015-0
[76] Boxma, O.J., Schlegel, S., and Yechiali, U., Two-queue Polling Models with a Patient Server, Ann. Oper. Res., 2002, vol. 112, no. 1–4, pp. 101–121. · Zbl 1013.90030 · doi:10.1023/A:1020929021474
[77] Boxma, O.J., Weststrate, J.A., and Yechiali, U., A Globally Gated Polling System with Server Interruptions, and Applications to the Repairman Problem, Prob. Eng. Inf. Sci., 1993, vol. 7, no. 2, pp. 187–208. · doi:10.1017/S0269964800002862
[78] Brill, P.H. and Hlynka, M., A Single Server N-line Queue in which a Customer May Receive Special Treatment, Commun. Stat.: Stochastic Models, 1998, vol. 14, no. 4, pp. 905–931. · Zbl 0910.60066 · doi:10.1080/15326349808807507
[79] Browne, S. and Kella, O., Parallel Service with Vacations, Oper. Res., 1995, vol. 43, no. 5, pp. 870–878. · Zbl 0842.90041 · doi:10.1287/opre.43.5.870
[80] Browne, S. and Weiss, G., Dynamic Priority Rules for Polling with Multiple Servers, Oper. Res. Lett., 1992, vol. 12, no. 3, pp. 129–138. · Zbl 0759.90035 · doi:10.1016/0167-6377(92)90096-L
[81] Browne, S. and Yechiali, U., Dynamic Scheduling in Single Server Multiclass Service Systems with Unit Buffers, Naval Res. Logistics, 1991, vol. 38, no. 3, pp. 383–396. · Zbl 0725.90033 · doi:10.1002/1520-6750(199106)38:3<383::AID-NAV3220380308>3.0.CO;2-D
[82] Bruneel, H. and Kim, B.G., Discrete-time Models for Communication Systems Including ATM, Boston: Kluwer, 1993.
[83] Bruno, R., Conti, M., and Gregory, E., Bluetooth: Architecture, Protocols and Scheduling Algorithms, Cluster Comput., 2002, vol. 5, pp. 117–131. · doi:10.1023/A:1013989524865
[84] Campbell, G.M., Cyclic Queuing Systems, Eur. J. Oper. Res., 1991, vol. 51, no. 2, pp. 155–167. · doi:10.1016/0377-2217(91)90246-R
[85] Chakravarthy, S.R., Analysis of a Priority Polling System with Group Services, Commun. Stat.: Stochastic Models, 1998, vol. 14, no. 1, pp. 25–49. · Zbl 0929.60075 · doi:10.1080/15326349808807459
[86] Chakravarthy, S.R. and Thiagarajan, S., Two Parallel Finite Queues with Simultaneous Services and Markovian Arrivals, J. Appl. Math. Stochastic Anal., 1997, vol. 10, no. 10, pp. 383–405. · Zbl 0896.60066 · doi:10.1155/S1048953397000439
[87] Chang, K.-H., First-come-first-served Polling Systems, Asia-Pacific J. Oper. Res., 2001, vol. 18, no. 1, pp. 1–11. · Zbl 1042.90530
[88] Chang, K.S., Stability Conditions for a Pipeline Polling Scheme in Satellite Communications, Queuing Syst., Theory Appl., 1993, vol. 14, no. 3–4, pp. 339–348. · Zbl 0798.90065 · doi:10.1007/BF01158872
[89] Chang, R.K.C. and Lam, S., A Novel Approach to Queue Stability Analysis of Polling Models, Performance Evaluat., 2000, vol. 40, no. 1–3, pp. 27–46. · Zbl 1052.68544 · doi:10.1016/S0166-5316(99)00068-1
[90] Chang, W. and Down, D.G., Exact Asymptotics for k i -limited Exponential Polling Models, Queuing Syst., 2002, vol. 42, no. 4, pp. 401–419. · Zbl 1013.90042 · doi:10.1023/A:1020993322286
[91] Chiarawongse, J. and Srinivasan, M.M., On Pseudo-conservation Laws for the Cyclic Server System with Compound Poisson Arrivals, Oper. Res. Lett., 1991, vol. 10, no. 8, pp. 453–459. · Zbl 0743.60095 · doi:10.1016/0167-6377(91)90022-H
[92] Choudhury, G.L. and Whitt, W., Computing Distributions and Moments in Polling Models by Numerical Transform Inversion, Performance Evaluat., 1996, vol. 25, no. 4, pp. 267–292. · Zbl 0900.68049 · doi:10.1016/0166-5316(95)00015-1
[93] Chung, H., Un, C., and Jung, W., Performance Analysis of Markovian Polling Systems with Single Buffers, Performance Evaluat., 1994, vol. 19, no. 4, pp. 303–315. · Zbl 0802.60090 · doi:10.1016/0166-5316(94)90044-2
[94] Coffman, E.G., Jr., Liu, Z., and Weber, R.R., Optimal Robot Scheduling for Web Search Engines, J. Scheduling, 1998, vol. 1, no. 1, pp. 15–29. · Zbl 0909.90174 · doi:10.1002/(SICI)1099-1425(199806)1:1<15::AID-JOS3>3.0.CO;2-K
[95] Coffman, E.G., Jr., Puhalskii, A.A., and Reiman, M.I., Polling Systems in Heavy Traffic: A Bessel Process Limit, Math. Oper. Res., 1998, vol. 23, no. 2, pp. 257–304. · Zbl 0981.60088 · doi:10.1287/moor.23.2.257
[96] Coffman, E.G., Jr., Puhalskii, A.A., and Reiman, M.I., Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle, Ann. Appl. Prob., 1995, vol. 5, no. 3, pp. 681–719. · Zbl 0842.60088 · doi:10.1214/aoap/1177004701
[97] Cooper, R.B., Niu, S.-C., and Srinivasan, M.M., A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive, Oper. Res., 1996, vol. 44, no. 4, pp. 629–633. · Zbl 0865.90065 · doi:10.1287/opre.44.4.629
[98] Cooper, R.B., Niu, S.-C., and Srinavasan, M.M., Setups in Polling Models: Does it Make Sense to Set up if no Work is Waiting?, J. Appl. Prob., 1999, vol. 36, pp. 585–592. · Zbl 0942.60087 · doi:10.1017/S0021900200017332
[99] Cooper, R.B., Niu, S.-C., and Srinavasan, M.M., Some Reflections on the Renewal-theory Paradox in Queuing Theory, J. Appl. Math. Stochastic Anal., 1998, vol. 11, no. 3, pp. 355–368. · Zbl 0915.60081 · doi:10.1155/S104895339800029X
[100] Cooper, R.B., Niu, S.-C., and Srinivasan, M.M., When Does Forced Idle Time Improve Performance in Polling Models?, Manag. Sci., 1998, vol. 44, no. 8, pp. 1079–1086. · Zbl 0989.90041 · doi:10.1287/mnsc.44.8.1079
[101] Daganzo, C.F., Some Properties of Polling Systems, Queuing Syst., 1990, vol. 6, no. 2, pp. 137–154. · Zbl 0712.60102 · doi:10.1007/BF02411470
[102] de Souza e Silva, E., Gail, R.H., and Muntz, R.R., Polling Systems with Server Timeouts and Their Application to Token Passing Networks, IEEE/ACM Trans. Networking, 1995, vol. 3, no. 5, pp. 560–575. · doi:10.1109/90.469950
[103] Delcoigne, F. and Fayolle, G., Thermodynamical Limit and Propagation of Chaos in Polling Systems, Markov Processes and Related Fields, 1999, vol. 5, no. 1, pp. 89–124. · Zbl 0920.60072
[104] Delcoigne, F. and la Fortelle, A., Large Deviations Rate Function for Polling Systems, Queuing Syst., 2002, vol. 41, no. 1–2, pp. 13–44. · Zbl 1053.60096 · doi:10.1023/A:1015781417451
[105] Deng, Q., A Two-queue E/1-L Polling Model with Regularly Varying Service and/or Switchover Times, Commun. Stat.: Stochastic Models, 2003, vol. 19, no. 4, pp. 507–526. · Zbl 1030.60083 · doi:10.1081/STM-120025402
[106] Dou, C. and Chang, J.-F., Serving Two Correlated Queues with a Synchronous Server under Exhaustive Service Discipline and Nonzero Switchover Time, IEEE Trans. Commun., 1991, vol. 39, no. 11, pp. 1582–1589. · doi:10.1109/26.111435
[107] Down, D., On the Stability of Polling Models with Multiple Servers, J. Appl. Prob., 1998, vol. 35, no. 4, pp. 925–935. · Zbl 0938.60096 · doi:10.1017/S0021900200016636
[108] Dror, H. and Yechiali, U., Closed Polling Models with Failing Nodes, Queuing Syst., 2000, vol. 35, no. 1–4, pp. 55–81. · Zbl 0966.90015 · doi:10.1023/A:1019181725107
[109] Duenyas, I., Gupta, D., and Olsen, T.L., Control of a Single-server Tandem Queuing System with Setups, Oper. Res., 1998, vol. 46, no. 2, pp. 218–230. · Zbl 0979.90031 · doi:10.1287/opre.46.2.218
[110] Duenyas, I. and van Oyen, M.P., Heuristic Scheduling of Parallel Heterogeneous Queues with Set-ups, Manag. Sci., 1996, vol. 42, no. 6, pp. 814–829. · Zbl 0880.90046 · doi:10.1287/mnsc.42.6.814
[111] Duenyas, I. and van Oyen, M.P., Stochastic Scheduling of Parallel Queues with Set-up Costs, Queuing Syst., 1995, vol. 19, pp. 421–444. · Zbl 0840.90075 · doi:10.1007/BF01151932
[112] Duffield, N.G., Exponents for the Tails of Distributions in Some Polling Models, Queuing Syst., 1997, vol. 26, no. 1–2, pp. 105–119. · Zbl 0901.60068 · doi:10.1023/A:1019120905658
[113] Eisenberg, M., The Polling System with a Stopping Server, Queuing Syst., 1994, vol. 18, no. 3–4, pp. 387–431. · Zbl 0836.90076 · doi:10.1007/BF01158769
[114] Eliazar, I., Gated Polling Systems with Levy Inflow and Inter-dependent Switchover Times: A Dynamical-Systems Approach, Queuing Syst., 2005, vol. 49, no. 1, pp. 49–72. · Zbl 1141.90356 · doi:10.1007/s11134-004-5555-7
[115] Eliazar, I., The Snowblower Problem, Queuing Syst., 2003, vol. 45, no. 4, pp. 357–380. · Zbl 1055.90014 · doi:10.1023/B:QUES.0000018027.64828.2d
[116] Eliazar, I., Fibich, G., and Yechiali, U., A Communication Multiplexer Problem: Two Alternating Queues with Dependent Randomly-timed Gated Regime, Queuing Syst., 2002, vol. 42, no. 4, pp. 325–353. · Zbl 1013.90045 · doi:10.1023/A:1020969804539
[117] Eliazar, I. and Yechiali, U., Polling under the Randomly-timed Gated Regime, Commun. Stat.: Stochastic Models, 1998, vol. 14, no. 1–2, pp. 79–93. · Zbl 0903.60083 · doi:10.1080/15326349808807461
[118] Fabian, O. and Levy, H., Pseudo-Cyclic Policies for Multi-queue Single Server Systems, Ann. Oper. Res., 1994, vol. 48, no. 1–4, pp. 127–152. · Zbl 0787.90029 · doi:10.1007/BF02023096
[119] Fayolle, G. and Lasgouttes, J.-M., A State-dependent Polling Model with Markovian Routing, IMA Volumes Math. Appl., 1995, vol. 71, pp. 283–301. · Zbl 0829.60080 · doi:10.1007/978-1-4757-2418-9_14
[120] Federgruen, A. and Katalan, Z., Approximating Queue Size and Waiting-time Distributions in General Polling Systems, Queuing Syst., 1994, vol. 18, no 3–4, pp. 353–386. · Zbl 0938.68544 · doi:10.1007/BF01158768
[121] Feng, W., Kowada, M., and Adachi, K., A Two-queue Model with Bernoulli Service Schedule and Switching Times, Queuing Syst., 1998, vol. 30, no. 3–4, pp. 405–434. · Zbl 0919.90065 · doi:10.1023/A:1019185509235
[122] Feng, W., Kowada, M., and Adachi, K., Analysis of a Multi-server Queue with Two Priority Classes and (M, N)-threshold Service Schedule I: Non-preemptive Priority, Int. Trans. Oper. Res., 2000, vol. 7, no. 6, pp. 653–671. · doi:10.1111/j.1475-3995.2000.tb00223.x
[123] Feng, W., Kowada, M., and Adachi, K., Performance Analysis of a Two-queue Model with an (M, N)-threshold Service Schedule, J. Oper. Res. Soc. Japan, 2001, vol. 44, no. 2, pp. 101–124. · Zbl 1038.90019
[124] Feng, W., Kowada, M., and Adachi, K., Two-queue and Two-server Model with a Hysteretic Control Service Policy, Sci. Math. Japonicae, 2001, vol. 54, no. 1, pp. 93–107. · Zbl 1010.60083
[125] Fischer, M.J., Harris, C.M., and Xie, J., An Interpolation Approximation for Expected Wait in a Time-limited Polling System, Comput. Oper. Res., 2000, vol. 27, no. 4, pp. 353–366. · Zbl 0973.90022 · doi:10.1016/S0305-0548(99)00056-8
[126] Foss, S. and Kovalevskii, A., A Stability Criterion via Fluid Limits and Its Application to a Polling System, Queuing Syst., 1999, vol. 32, no. 1–3, pp. 131–168. · Zbl 0945.90013 · doi:10.1023/A:1019187004209
[127] Foss, S. and Last, G., On the Stability of Greedy Polling Systems with General Service Policies, Prob. Eng. Inf. Sci., 1998, vol. 12, no. 1, pp. 49–68. · Zbl 0962.60099 · doi:10.1017/S0269964800005052
[128] Foss, S. and Last, G., Stability of Polling Systems with Exhaustive Service Policies and State-dependent Routing, Ann. Appl. Prob., 1996, vol. 6, no. 1, pp. 116–137. · Zbl 0863.60091 · doi:10.1214/aoap/1034968068
[129] Fournier, L. and Rosberg, Z., Expected Waiting Times in Cyclic Service Systems under Priority Disciplines, Queuing Syst., 1991, vol. 9, no. 4, pp. 419–439. · Zbl 0732.60106 · doi:10.1007/BF01159225
[130] Frigui, I. and Alfa, A.S., Analysis of a Discrete Time Table Polling System with MAP Input and Time-limited Service Discipline, Telecommunication Syst., 1999, vol. 12, no. 1, pp. 51–77. · doi:10.1023/A:1019182325899
[131] Frigui, I. and Alfa, A.S., Analysis of Time-limited Polling System, Comput. Commun., 1998, vol. 21, no. 6, pp. 558–571. · Zbl 05396453 · doi:10.1016/S0140-3664(98)00128-5
[132] Fuhrmann, S.W., A Decomposition Result for a Class of Polling Models, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 109–120. · Zbl 0752.60078 · doi:10.1007/BF01159290
[133] Fuhrmann, S.W. and Moon, A., Queues Served in Cyclic Order with an Arbitrary Start-up Distribution, Naval Res. Logistics, 1990, vol. 37, no. 1, pp. 123–133. · Zbl 0684.60074 · doi:10.1002/1520-6750(199002)37:1<123::AID-NAV3220370108>3.0.CO;2-N
[134] Fuhrmann, S.W. and Wang, Y.T., Analysis of Cyclic Service Systems with Limited Service: Bounds and Approximations, Performance Evaluat., 1988, vol. 8, pp. 35–54. · Zbl 0651.90032 · doi:10.1016/0166-5316(88)90023-5
[135] Gandhi, A.D. and Cassandras, C.G., Optimal Control of Polling Models for Transportation Applications, Math. Comput. Modelling, 1996, vol. 23, no. 11–12, pp. 1–23. · Zbl 0857.93097 · doi:10.1016/0895-7177(96)00062-3
[136] Georgiadis, L. and Szpankowski, W., Stability of Token Passing Rings, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 7–33. · Zbl 0748.68004 · doi:10.1007/BF01159285
[137] Grasman, S.E., Olsen, T.L., and Birge, J.R., Finite Buffer Polling Models with Routing, Eur. J. Oper. Res., 2005, vol. 165, no. 3, pp. 794–809. · Zbl 1062.90016 · doi:10.1016/j.ejor.2003.11.030
[138] Grelá-M’Poko, B., Mehmet Ali, M., and Hayes, J.F., Approximate Analysis of Asymmetric Single-Service Prioritized Token Passing Systems, IEEE Trans. Commun., 1991, vol. 39, no. 7, pp. 1037–1040. · doi:10.1109/26.87207
[139] Grillo, D., Polling Mechanism Models in Communication Systems–Some Application Examples, in Stochastic Analysis of Computer and Communication Systems, Takagi, H., Ed., Amsterdam: North-Holland, 1990, pp. 659–698.
[140] Groenendijk, W.P. and Levy, H., Performance Analysis of Transaction Driven Computer Systems via Queuing Analysis of Polling Models, IEEE Trans. Comput., 1992, vol. 41, no. 4, pp. 455–466. · doi:10.1109/12.135558
[141] Günalay, Y. and Gupta, D., Polling System with Patient Server and State-dependent Setup Times, IIE Trans., 1997, vol. 29, no. 6, pp. 469–480.
[142] Günalay, Y. and Gupta, D., Threshold Start-up Control Policy for Polling Systems, Queuing Syst., 1998, vol. 29, no. 2–4, pp. 399–421. · Zbl 0917.90130 · doi:10.1023/A:1019152601966
[143] Gupta, D. and Buzacott, J.A., A Production System with Two Job Classes, Changeover Times and Revisitation, Queuing Syst., 1990, vol. 6, no. 4, pp. 353–368. · Zbl 0825.90526 · doi:10.1007/BF02411483
[144] Gupta, D. and Günalay, Y., Recent Advances in the Analysis of Polling Systems, in Advances in Combinatorial Methods with Applications to Probability and Statistics, Special Edition, Boston: Birkhauser, 1996, pp. 339–360. · Zbl 0894.60093
[145] Gupta, D., Günalay, Y., and Srinivasan, M.M., The Relationship Between Preventive Maintenance and Manufacturing System Performance, Eur. J. Oper. Res., 2001, vol. 132, no. 1, pp. 146–162. · Zbl 0991.90051 · doi:10.1016/S0377-2217(00)00118-1
[146] Gupta, D. and Srinivasan, M.M., Polling Systems with State-dependent Setup Times, Queuing Syst., 1996, vol. 22, no. 3–4, pp. 403–423. · Zbl 0860.60081 · doi:10.1007/BF01149181
[147] Harel, A. and Stulman, A., Polling, Greedy and Horizon Servers on a Circle, Queuing Syst., 1995, vol. 43, no. 1, pp. 177–186. · Zbl 0830.90056
[148] Hirayama, T., Hong, S.J., and Krunz, M.M., A New Approach to Analysis of Polling Systems, Queuing Syst., 2004, vol. 48, no. 1–2, pp. 89–102. · Zbl 1061.60096 · doi:10.1023/B:QUES.0000039891.78286.dd
[149] Hwang, L.-C. and Chang, C.-J., An Exact Analysis of an Asymmetric Polling System with Mixed Service Discipline and General Service Order, Comput Commun., 1997, vol. 20, pp. 1292–1300. · doi:10.1016/S0140-3664(97)00110-2
[150] Ibe, O.C., Analysis of Polling Systems with Mixed Service Discipline, Commun. Stat.: Stochastic Models, 1990, vol. 6, no. 4, pp. 667–689. · Zbl 0708.60088 · doi:10.1080/15326349908807168
[151] Ibe, O.C. and Cheng, X., Approximate Analysis of Asymmetric Single-service Token Passing Systems, IEEE Trans. Commun., 1989, vol. 37, no. 6, pp. 572–577. · doi:10.1109/26.31141
[152] Ibe, O.C. and Trivedi, K.S., Stochastic Petri Net Models of Polling Systems, IEEE J. Selected Areas Commun., 1990, vol. 8, no. 9, pp. 1649–1657. · doi:10.1109/49.62852
[153] Ibe, O.C. and Trivedi, K.S., Two Queues with Alternating Service and Server Breakdown, Queuing Syst., 1990, vol. 7, no. 3, pp. 253–268. · Zbl 0712.60101 · doi:10.1007/BF01154545
[154] Itai, A. and Rosberg, Z., A Golden Ratio Control Policy for a Multiple-acess Channel, IEEE Trans. Automat. Control., 1984, vol. 29, pp. 712–718. · Zbl 0542.90036 · doi:10.1109/TAC.1984.1103619
[155] Jiang, Y., Tham, C.-K., and Ko, C.-C., Delay Analysis of a Probabilistic Priority Discipline, Eur. Trans. Telecommun., 2002, vol. 13, no. 6, pp. 563–577. · doi:10.1002/ett.4460130603
[156] Jirachiefpattana, A., County, P., Dillon, T.S., and Lai, R., Performance Evaluation of PC Routers Using a Single-server Multi-queue System with a Reflection Technique, Comput. Commun., 1997, vol. 20, no. 1, pp. 1–10. · doi:10.1016/S0140-3664(97)83569-4
[157] Jung, W.Y. and Un, C.K., Analysis of a Finite-buffer Polling System with Exhaustive Service Based on Virtual Buffering, IEEE Trans. Commun., 1994, vol. 42, no. 12, pp. 3144–3149. · doi:10.1109/26.339835
[158] Karvelas, D., Leon-Garcia, A., Delay Analysis of Various Service Disciplines in Symmetric Token Passing Networks, IEEE Trans. Commun., 1993, vol. 41, no. 9, pp. 1342–1355. · Zbl 0800.94333 · doi:10.1109/26.237853
[159] Katayama, T., Performance Analysis and Optimization of a Cyclic-Service Tandem Queuing System with Multi-class Customers, Comput. Math. Appl., 1992, vol. 24, no. 1/2, pp. 25–33. · Zbl 0782.60061 · doi:10.1016/0898-1221(92)90224-6
[160] Khalid, M., Vyavahare, P.D., and Kerke, H.B., Analysis of Asymmetric Polling Systems, Comput. Oper. Res., 1997, vol. 42, no. 4, pp. 317–333. · Zbl 0891.90068 · doi:10.1016/S0305-0548(96)00057-3
[161] Khamisy, A., Altman, E., and Sidi, M., Polling Systems with Synchronization Constraints, Ann. Oper. Res., 1992, vol. 35, no. 1–4, pp. 231–267. · Zbl 0755.60084 · doi:10.1007/BF02188706
[162] Khamisy, A. and Sidi, M., Discrete-time Priority Queues with Two-state Markov Modulated Arrivals, Commun. Stat.: Stochastic Models, 1992, vol. 8, no. 2, pp. 337–357. · Zbl 0751.60091 · doi:10.1080/15326349208807228
[163] Kim, E. and van Oyen, M.P., Beyond the c\(\mu\) Rule: Dynamic Scheduling of a Two-class Loss Queue, Math. Methods Oper. Res., 1997, vol. 48, no. 1, pp. 17–36. · Zbl 0947.90027 · doi:10.1007/PL00003992
[164] Kim, E., van Oyen, M.P., and Rieders, M., General Dynamic Programming Algorithms Applied to Polling Systems, Commun. Stat.: Stochastic Models, 1998, vol. 14, no. 5, pp. 1197–1221. · Zbl 0912.90137 · doi:10.1080/15326349808807520
[165] Kofman, D. and Yechiali, U., Polling with Stations Breakdowns, Performance Evaluat., 1996, vol. 27–28, no. 4, pp. 647–672. · Zbl 0900.68033 · doi:10.1016/S0166-5316(96)90050-4
[166] Konheim, A.G. and Meister, B., Waiting Lines and Times in a System with Polling, J. ACM, 1974, vol. 21, no. 3, pp. 470–490. · Zbl 0298.68047 · doi:10.1145/321832.321845
[167] Kohneim, A.G., Levy, H., and Srinivasan, M.M., Descendant Set: An Efficient Approach for the Analysis of Polling Systems, IEEE Trans. Commun., 1994, vol. 42, no. 2–4, pp. 1245–1253. · doi:10.1109/TCOMM.1994.580233
[168] Koole, G., Assigning a Single Server to Inhomogeneous Queues with Switching Costs, Theoretical Comput. Sci., 1997, vol. 182, no. 1–2, pp. 203–216. · Zbl 0901.68016 · doi:10.1016/S0304-3975(96)00186-7
[169] Koole, G. and Nain, Ph., On the Value Function of a Priority Queue with an Application to a Controlled Polling Model, Queuing Syst., 2000, vol. 34, no. 1–4, pp. 199–214. · Zbl 0942.90016 · doi:10.1023/A:1019109103725
[170] Kopsel, A., Ebert, J.-P., and Wolisz, A., A Performance Comparison of Point and Distributed Function of an IEEE 802.11 WLAN in the Presence of Real-time Requirements, Proc. Inf. Workshop MoMuc2000, Waseda, Japan, October 2000.
[171] Kroese, D.P., Heavy Traffic Analysis for Continuous Polling Models, J. Appl. Prob., 1997, vol. 34, no. 3, pp. 720–732. · Zbl 0886.60092 · doi:10.1017/S0021900200101378
[172] Kroese, D.P. and Schmidt, V., A Continuous Polling System with General Service Times, Ann. Appl. Prob., 1992, vol. 2, no. 4, pp. 906–927. · Zbl 0772.60075 · doi:10.1214/aoap/1177005580
[173] Kudoh, S., Takagi, H., and Hashida, O., Second Moments of the Waiting Time in Symmetric Polling Systems, J. Operat. Res. Soc. Japan, 2000, vol. 43, no. 2, pp. 306–316. · Zbl 1138.90363 · doi:10.15807/jorsj.43.306
[174] Landry, R. and Stavrakakis, I., Queuing Study of 3-priority Policy with Distinct Service Strategies, IEEE/ACM Trans. Networking, 1993, vol. 1, no. 5, pp. 576–589. · doi:10.1109/90.251916
[175] Langaris, C., A Polling Model with Retrial Customers, J. Oper. Res. Soc. Japan, 1997, vol. 40, no. 4, pp. 489–508. · Zbl 0905.90067
[176] Langaris, C., Gated Polling Models with Customers in Orbit, Math. Comput. Modeling, 1999, vol. 30, no. 3–4, pp. 171–187. · Zbl 1042.60542 · doi:10.1016/S0895-7177(99)00140-5
[177] Langaris, C., Markovian Polling Systems with Mixed Service Discipline and Retrial Customers, TOP, 1999, vol. 7, pp. 305–322. · Zbl 0949.60096 · doi:10.1007/BF02564729
[178] Lee, D.-S., A Two-queue Model with Exhaustive and Limited Service Disciplines, Commun. Stat.: Stochastic Models, 1996, vol. 12, no. 2, pp. 285–305. · Zbl 0852.60099 · doi:10.1080/15326349608807385
[179] Lee, D.-S., Analysis of a Two-queue Model with Bernoulli Schedules, J. Appl. Prob., 1997, vol. 34, no. 1, pp. 176–191. · Zbl 0871.90033 · doi:10.1017/S0021900200100804
[180] Lee, D-S. and Sengupta, B., An Approximate Analysis of a Cyclic Server Queue with Limited Service and Reservations, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 153–178. · Zbl 0752.60080 · doi:10.1007/BF01159293
[181] Lee, D-S. and Sengupta, B., Queuing Analysis of a Threshold Based Priority Scheme for ATM Networks, IEEE Trans. Networking, 1993, vol. 1, no. 6, pp. 709–717. · doi:10.1109/90.266058
[182] Lee, T., Analysis of Infinite Servers Polling Systems with Correlated Input Process and State Dependent Vacations, Eur. J. Oper. Res., 1999, vol. 115, no. 2, pp. 392–412. · Zbl 0938.90014 · doi:10.1016/S0377-2217(98)00199-4
[183] Lee, T., Analysis of Random Polling Systems with Infinite Coupled Servers and Correlated Input Process, Comput. Oper. Res., 2003, vol. 30, no. 13, pp. 2003–2020. · Zbl 1047.90016 · doi:10.1016/S0305-0548(02)00121-1
[184] Lee, T., A Closed Form Solution for the Asymmetric Random Polling System with Correlated Levy Input Process, Math. Oper. Res., 1997, vol. 22, no. 2, pp. 432–457. · Zbl 0884.60087 · doi:10.1287/moor.22.2.432
[185] Lee, T., Models for Design and Control of Single Server Polling Computer and Communication Systems, Oper. Res., 1998, vol. 46, pp. 515–531. · Zbl 0982.90016 · doi:10.1287/opre.46.4.515
[186] Lee, T. and Sunjaya, J., Exact Analysis of Asymmetric Random Polling Systems with Single Buffers and Correlated Levy Input Process, Queuing Syst., 1996, vol. 23, no. 3–4, pp. 131–156. · Zbl 0877.90038 · doi:10.1007/BF01206554
[187] Leung, K.K., Cyclic Service Systems with Non-preemptive, Time-limited Service, IEEE Trans. Commun., 1994, vol. 42, no. 8, pp. 2521–2524. · doi:10.1109/26.310608
[188] Leung, K.K., Cyclic Service Systems with Probabilistically-limited Service, IEEE J. Selected Areas Commun., 1991, vol. 9, no. 2, pp. 185–193. · doi:10.1109/49.68446
[189] Levy, H., Analysis of Cyclic Polling Systems with Binomial-gated Service, in Performance of Distributed Parallel Systems, Amsterdam: Elsevier, 1989, pp. 127–139.
[190] Levy, H., Binomial-gated Service: A Method for Effective Operation and Optimization of Polling Systems, IEEE Trans. Commun., 1991, vol. 39, no. 9, pp. 1341–1350. · doi:10.1109/26.99140
[191] Levy, H. and Kleinrock, L., Polling Systems with Zero Switch-over Periods: A General Method for Analysis the Expected Delay, Performance Evaluat., 1991, vol. 13, no. 2, pp. 97–107. · Zbl 0752.90024 · doi:10.1016/0166-5316(91)90043-3
[192] Levy, H. and Sidi, M., Polling Systems: Applications, Modeling and Optimization, IEEE Trans. Commun., 1990, vol. 38, no. 10, pp. 1750–1760. · doi:10.1109/26.61446
[193] Levy, H. and Sidi, M., Polling Systems with Simultaneous Arrivals, IEEE Trans. Commun., 1991, vol. 39, no. 6, pp. 823–827. · doi:10.1109/26.87170
[194] Levy, H., Sidi, M., and Boxma, O.J., Dominance Relations in Polling Systems, Queuing Syst., 1990, vol. 6, no. 2, pp. 155–171. · Zbl 0712.60103 · doi:10.1007/BF02411471
[195] Liu, Z. and Nain, P., Optimal Scheduling in Some Multi-queue Single-server Systems, IEEE Trans. Automat. Control, 1992, vol. 37, no. 2, pp. 247–252. · doi:10.1109/9.121629
[196] Liu, Z., Nain, P., and Towsley, D., On Optimal Polling Policies, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 59–83. · Zbl 0752.60082 · doi:10.1007/BF01159287
[197] Lye, K. and Seah, K., Random Polling Scheme with Priority, Electronic Lett., 1992, vol. 28, no. 14, pp. 1290, 1291. · doi:10.1049/el:19920820
[198] Magalhaes, M.N., McNickle, D.C., and Salles, M.C.B., Outputs from a Loss System with Two Stations and a Smart (Cyclic) Server, Investigacion Oper., 1998, vol. 16, no. 1–3, pp. 111–126.
[199] Markowitz, D.M. and Wein, L.M., Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem, Oper. Res., 2001, vol. 49, no. 2, pp. 246–270. · Zbl 1163.90499 · doi:10.1287/opre.49.2.246.13530
[200] Massoulie, L., Stability of Non-Markovian Polling Systems, Queuing Syst., 1995, vol. 21, no. 1–2, pp. 67–95. · Zbl 0851.60089 · doi:10.1007/BF01158575
[201] Menshikov, M. and Zuyev, S., Polling Systems in Critical Regime, Stoch. Proc. Appl., 2001, vol. 92, pp. 201–218. · Zbl 1047.60036 · doi:10.1016/S0304-4149(00)00087-9
[202] Miorandi, D., Zanella, A., and Pierobon, G., Performance Evaluation of Bluetooth Polling Schemes: An Analytical Approach, ACM Mobile Networks Appl., 2004, vol. 9, no. 2, pp. 63–72. · Zbl 02040452 · doi:10.1023/A:1027373823773
[203] Murata, M., Shiomoto, K., and Miyahara, H., Performance Analysis of Token Ring Networks with a Reservation Priority Discipline, IEEE Trans. Commun., 1990, vol. 38, no. 10, pp. 1844–1853. · doi:10.1109/26.61455
[204] Nakdimon, O. and Yechiali, U., Polling Systems with Breakdowns and Repairs, Eur. J. Oper. Res., 2001, vol. 149, no. 3, pp. 588–613. · Zbl 1033.90021 · doi:10.1016/S0377-2217(02)00451-4
[205] Olsen, T.L., Approximations for the Waiting Time Distribution in Polling Models with and without State-dependent Setups, Oper. Res. Lett., 2001, vol. 28, no. 3, pp. 113–123. · Zbl 0996.60100 · doi:10.1016/S0167-6377(01)00058-X
[206] Olsen, T.L., Limit Theorems for Polling Models with Increasing Setups, Prob. Eng. Inf. Sci., 2001, vol. 15, no. 1, pp. 35–55. · Zbl 1087.90507 · doi:10.1017/S026996480115103X
[207] Olsen, T.L. and van Der Mei, R.D., Polling Systems with Periodic Server Routing in Heavy Traffic: Distribution of the Delay, J. Appl. Prob., 2003, vol. 40, no. 2, pp. 305–326. · Zbl 1127.60315 · doi:10.1017/S002190020001932X
[208] Olsen, T.L. and van Der Mei, R.D., Polling Systems with Periodic Server Routing in Heavy-Traffic: Renewal Arrivals, Oper. Res. Lett., 2005, vol. 33, no. 1, pp. 17–25. · Zbl 1076.90011 · doi:10.1016/j.orl.2004.05.003
[209] Ozawa, T., Alternating Service Queues with Mixed Exhaustive and k-limited Service, Performance Evaluat., 1990, vol. 11, no. 3, pp. 165–175. · doi:10.1016/0166-5316(90)90009-8
[210] Park, B.U., Ryu, W., Kim, D.-U., Lee, B.L., and Chung, J.-W., Two Priority Class Polling Systems with Batch Poisson Arrivals, Korean Commun. Stat., 1999, vol. 6, no. 3, pp. 881–891.
[211] Peköz, E., More on Using Forced to Idle Time to Improve Performance in Polling Models, Prob. Eng. Inf. Sci., 1999, vol. 13, no. 4, pp. 489–496. · Zbl 0969.90040 · doi:10.1017/S0269964899134053
[212] Qiao, D., Choi, S., Soomoro, A., and Shin, K.G., Energy-efficient PCF Operation of IEEE 802.11a Wireless LAN, Proc. INFO COM 2002, New York, June 2002.
[213] Reiman, M. and Wein, L., Dynamic Scheduling of a Two-class Queue with Setups, Oper. Res., 1998, vol. 46, no. 4, pp. 532–547. · Zbl 0979.90023 · doi:10.1287/opre.46.4.532
[214] Reiman, M. and Wein, L., Heavy Traffic Analysis of Polling Systems in Tandem, Oper. Res., 1999, vol. 47, no. 4, pp. 524–534. · Zbl 0979.90018 · doi:10.1287/opre.47.4.524
[215] Resing, J.A.C., Polling Systems and Multitype Branching Processes, Queuing Syst., 1993, vol. 13, no. 4, pp. 409–426. · Zbl 0772.60069 · doi:10.1007/BF01149263
[216] Rubin, I. and Tsai, Z., Performance of Token Schemes Supporting Delay Constrained Priority Traffic Streams, IEEE Trans. Commun., 1990, vol. 38, no. 11, pp. 1994–2003. · doi:10.1109/26.61482
[217] Rykov, V.V., Monotone Control of Queuing Systems with Heterogeneous Servers, Queuing Syst., 2001, vol. 37, no. 4, pp. 391–403. · Zbl 1017.90026 · doi:10.1023/A:1010893501581
[218] Ryu, W., Jun, K.P., Kim, D.W., and Park, B.U., Waiting Times in Priority Polling Systems with Batch Poisson Arrivals, Korean Commun. Stat., 1998, vol. 5, no. 3, pp. 809–817.
[219] Sarkar, D., Zangwill, W.I., Variance Effects in Cyclic Production Systems, Manag. Sci., 1991, vol. 37, no. 4, pp. 444–453. · doi:10.1287/mnsc.37.4.444
[220] Schassberger, R., Stability of Polling Networks with State-dependent Server Routing, Prob. Eng. Inf. Sci., 1995, vol. 9, no. 4, pp. 539–550. · Zbl 1336.68023 · doi:10.1017/S0269964800004046
[221] Sharafali, M., Co, H.C., and Goh, M., Production Scheduling in a Flexible Manufacturing System under Random Demand, Eur. J. Oper. Res., 2004, vol. 158, no. 1, pp. 89–102. · Zbl 1061.90039 · doi:10.1016/S0377-2217(03)00300-X
[222] Sharma, V., Stability and Continuity of Polling Systems, Queuing Syst., 1994, vol. 16, no. 1–2, pp. 115–137. · Zbl 0794.60093 · doi:10.1007/BF01158952
[223] Shimogawa, S. and Takahashi, T., A Note on the Pseudo-conservation Law for a Multi-queue with Local Priority, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 145–151. · Zbl 0752.60084 · doi:10.1007/BF01159292
[224] Shiozawa, Y., Takine, T., Takahashi, Y., and Hasegawa, T., Analysis of a Polling System with Correlated Input, Computer Networks ISDN Syst., 1990, vol. 20, no. 1–5, pp. 297–308. · doi:10.1016/0169-7552(90)90038-T
[225] Sidi, M., Levy, H., and Fuhrmann, S.W., A Queuing Network with a Single Cyclically Roving Server, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 121–144. · Zbl 0752.60069 · doi:10.1007/BF01159291
[226] Singh, M.P. and Srinivasan, M.M., Exact Analysis of the State Dependent Polling Model, Queuing Syst., 2002, vol. 41, no. 4, pp. 371–399. · Zbl 0993.90025 · doi:10.1023/A:1016287431905
[227] Srinivasan, M.M., Nondeterministic Polling Systems, Manag. Sci., 1991, vol. 37, no. 6, pp. 667–681. · Zbl 0755.90032 · doi:10.1287/mnsc.37.6.667
[228] Srinivasan, M.M., Niu, S.-C., and Cooper, R.B., Relating Polling Models with Nonzero Switchover Times, Queuing Syst., 1995, vol. 19, pp. 149–168. · Zbl 0820.60077 · doi:10.1007/BF01148944
[229] Stavrakakis, I. and Tsakiridou, S., Study of a Class of Partially Ordered Service Strategies for a System of Two Discrete-time Queues, Performance Evaluat., 1997, vol. 29, no. 1, pp. 15–33. · Zbl 0900.68054 · doi:10.1016/S0166-5316(96)00002-8
[230] Suk, J.B. and Cassandras, C.G., Optimal Scheduling of Two Competing Queues with Blocking, IEEE Trans. Automat. Control, 1991, vol. 36, no. 9, pp. 1086–1091. · Zbl 0739.60087 · doi:10.1109/9.83545
[231] Suzuki, S. and Yamashita, H., Mean Waiting Times of the Alternating Traffic Starting Delays, J. Oper. Res. Soc. Japan, 1998, vol. 41, no. 3, pp. 442–454. · Zbl 1138.90340
[232] Takagi, H., Analysis and Applications of Polling Models, in Performance Evaluation: Origins and Directions. Lecture Notes Comput. Sci., Haring, G., Lindemann, Ch., and Reiser, M., Eds., 2000, vol. 1769, pp. 423–442.
[233] Takagi, H., Analysis of an M/G/1//N Queue with Multiple Server Vacations, and Its Application to a Polling Model, J. Oper. Res. Soc. Japan, 1992, vol. 35, pp. 300–315. · Zbl 0771.60085
[234] Takagi, H., Analysis of Polling Systems, Cambridge: MIT Press, 1986.
[235] Takagi, H., Applications of Polling Models to Computer Networks, Comput. Networks ISDN Syst., 1991, vol. 22, no. 3, pp. 193–211. · doi:10.1016/0169-7552(91)90087-S
[236] Takagi, H., Queuing Analysis of Polling Systems, ACM Comput. Surveys, 1988, vol. 20, no. 1, pp. 5–28. · Zbl 0649.68032 · doi:10.1145/62058.62059
[237] Takagi, H., Queuing Analysis of Polling Models: An Update, in Stochastic Analysis of Computer and Communication Systems, Takagi, H., Ed., Amsterdam: North-Holland, 1990, pp. 267–318.
[238] Takagi, H., Queuing Analysis of Polling Models: Progress in 1990–1994, in Frontiers in Queuing, Dshalalow, J.H., Ed., Boca Raton: CRC, 1997, pp. 119–146. · Zbl 0871.60077
[239] Takahashi, Y., Fujimoto, K., and Makimoto, N., Geometric Decay of the Steady-state Probabilities in a Quasi-birth-and-death Process with a Countable Number of Phases, Commun. Stat.: Stochastic Models, 2001, vol. 17, no. 1, pp. 1–24. · Zbl 0985.60074 · doi:10.1081/STM-100001397
[240] Takahashi, Y. and Kumar, B.K., Pseudo-conservation Law for Discrete-time Multi-queue System with Priority Disciplines, J. Oper. Res. Soc. Japan, 1995, vol. 38, no. 4, pp. 450–466. · Zbl 0849.90066
[241] Takine, T. and Hasewaga, T., A Cyclic-Service Finite Source Model with Round-robin Scheduling, Queuing Syst., 1992, vol. 11, no. 1–2, pp. 91–108. · Zbl 0752.60085 · doi:10.1007/BF01159289
[242] Takine, T. and Hasewaga, T., Average Waiting Time of a Symmetrical Polling System under Bernoulli Scheduling, Oper. Res. Lett., 1991, vol. 10, no. 9, pp. 535–539. · Zbl 0744.60115 · doi:10.1016/0167-6377(91)90074-Y
[243] Takine, T., Takagi, H., and Hasegawa, T., Sojourn Times in Vacation and Polling Systems with Bernoulli Feedback, J. Appl. Prob., 1991, vol. 28, no. 2, pp. 422–432. · Zbl 0733.60113 · doi:10.1017/S0021900200039796
[244] Takine, T., Takagi, H., Takahashi, Y., and Hasegawa, T., Analysis of Asymmetric Single-buffer Polling and Priority Systems without Switchover Times, Performance Evaluat., 1990, vol. 11, no. 4, pp. 253–264. · doi:10.1016/0166-5316(90)90003-2
[245] Takine, T., Takahashi, Y., and Hasegawa, T., Modeling and Analysis of a Single-buffer Polling System Interconnected with External Networks, INFOR, 1990, vol. 28, no. 3, pp. 166–177. · Zbl 0718.68015
[246] Tassiulas, L. and Ephremides, A., Dynamic Server Allocation to Parallel Queues with Randomly Varying Connectivity, IEEE Trans. Inf. Theory, 1993, vol. 39, no. 2, pp. 466–478. · Zbl 0800.94059 · doi:10.1109/18.212277
[247] Tedijanto, T.E., Exact Results for the Cyclic-service Queue with a Bernoulli Schedule, Performance Evaluat., 1990, vol. 11, no. 2, pp. 107–115. · doi:10.1016/0166-5316(90)90017-D
[248] Tran-Gia, P., Analysis of Polling Systems with General Input Process and Finite Capacity, IEEE Trans. Commun., 1992, vol. 40, no. 2, pp. 337–344. · doi:10.1109/26.129195
[249] Tseng, K.H. and Hsiao, M.-T.T., Optimal Control of Arrivals to Token Ring Networks with Exhaustive Service Discipline, Oper. Res., 1995, vol. 43, no. 1, pp. 89–101. · Zbl 0838.90050 · doi:10.1287/opre.43.1.89
[250] van der Heijden, M.C., Harten, A., and Ebben, M.J.R., Waiting Times at Periodically Switched Oneway Traffic Lanes–A Periodic, Two-queue Polling System with Random Setup Times, Prob. Eng. Inf. Sci., 2001, vol. 15, no. 4, pp. 495–517. · Zbl 1003.90011
[251] van der Mei, R.D., Delay in Polling Systems with Large Switch-over Times, J. Appl. Prob., 1999, vol. 36, no. 1, pp. 232–243. · Zbl 0955.60095 · doi:10.1017/S0021900200016995
[252] van der Mei, R.D., Distribution of the Delay in Polling Systems in Heavy Traffic, Performance Evaluat., 1999, vol. 38, no. 2, pp. 133–148. · Zbl 1017.68025 · doi:10.1016/S0166-5316(99)00048-6
[253] van der Mei, R.D., Polling Systems in Heavy Traffic: Higher Moments of the Delay, Queuing Syst., 1999, vol. 31, no. 3–4, pp. 265–294. · Zbl 0934.90024 · doi:10.1023/A:1019166432434
[254] van der Mei, R.D., Polling Systems with Periodic Server Routing in Heavy Traffic, Commun. Stat.: Stochastic Models, 1999, vol. 15, no. 2, pp. 273–297. · Zbl 0931.60078 · doi:10.1080/15326349908807537
[255] van der Mei, R.D., Polling Systems with Switch-over Times under Heavy Load: Moments of the Delay, Queuing Syst., 2000, vol. 36, no. 4, pp. 381–404. · Zbl 0974.60078 · doi:10.1023/A:1011041520533
[256] van der Mei, R.D., Waiting-time Distributions in Polling Systems with Simultaneous Batch Arrivals, Ann. Oper. Res., 2002, vol. 113, no. 1–4, pp. 155–173. · Zbl 1013.90019 · doi:10.1023/A:1020918230560
[257] van der Mei, R.D. and Borst, S.C., Analysis of Multiple-server Polling Systems by Means of the Power-series Algorithm, Commun. Stat.: Stochastic Models, 1997, vol. 13, no. 2, pp. 339–369. · Zbl 0880.60093 · doi:10.1080/15326349708807430
[258] van der Mei, R.D. and Levy, H., Expected Delay Analysis of Polling Systems in Heavy Traffic, Advances Appl. Prob., 1998, vol. 30, no. 2, pp. 586–602. · Zbl 0911.60079 · doi:10.1017/S0001867800047443
[259] van der Mei, R.D. and Levy, H., Polling Systems in Heavy Traffic: Exhaustiveness of Service Policies, Queuing Syst., 1997, vol. 27, no. 3–4, pp. 227–250. · Zbl 0905.90079 · doi:10.1023/A:1019118232492
[260] van der Wal, J. and Yechiali, U., Dynamic Visit-order Rules for Batch-service Polling, Prob. Eng. Inf. Sci., 2003, vol. 17, no. 3, pp. 351–367. · Zbl 1336.90027
[261] van Mieghem, J.A., Dynamic Scheduling with Convex Delay Costs: The Generalized c\(\mu\) Rule, Ann. Appl. Prob., 1995, vol. 5, no. 3, pp. 809–833. · Zbl 0843.90047 · doi:10.1214/aoap/1177004706
[262] van Oyen, M.P., Monotonicity of Optimal Performance Measures for Polling Systems, Prob. Eng. Inf. Sci., 1997, vol. 11, no. 2, pp. 219–228. · Zbl 1096.60524 · doi:10.1017/S0269964800004770
[263] van Oyen, M.P., and Teneketzis, D., Optimal Batch Service of a Polling System under Partial Information, Zeitschrift Oper. Res., 1996, vol. 44, no. 3, pp. 401–419. · Zbl 0867.90056
[264] Vishnevsky, V.M. and Lyakhov, A.I., Adaptive Features of IEEE 802.11 Protocol: Utilization, Tuning and Modifications, Proc. of 8th HP-OVUA Conf., Berlin, June 2001.
[265] Vishnevsky, V.M., Lyakhov, A.I., and Bakanov, A.S., Method for Performance Evaluation of Wireless Networks with Centralized Control, Proc. Int. Conf. ”Distributed Computer Communication Networks (Theory and Applications)” (DCNN’99), Tel-Aviv, Israel, November 9–13, 1999, pp. 189–194.
[266] Vishnevsky, V.M., Lyakhov, A.I., and Guzakov, N.N., An Adaptive Polling Strategy for IEEE 802.11 PCF, Proc. 7th Int. Symp. on Wireless Personal Multimedia Communications (WPMC’04), Abano Terme, Italy, September 12–15, 2004, vol. 1, pp. 87–91.
[267] Weststrate, J.A. and van der Mei, R.D., Waiting Times in a Two-queue Model with Exhaustive and Bernoulli Service, Zeitschrift für Operations Research (ZOR)–Math. Methods Oper. Res., 1994, vol. 40, no. 3, pp. 289–303. · Zbl 0832.60089 · doi:10.1007/BF01432970
[268] Xia, C.H., Michailidis, G., Bambos, N., and Glynn, P.W., Optimal Control of Parallel Queues with Batch Service, Prob. Eng. Inf. Sci., 2002, vol. 16, no. 3, pp. 289–307. · Zbl 1019.90016 · doi:10.1017/S0269964802163029
[269] Yechiali, U., Analysis and Control of Polling Systems, in Performance Evaluation of Computer and Communication Systems, Donatiello, L. and Nelson, R., Eds., Berlin: Springer, 1993, pp. 630–650.
[270] Yechiali, U. and Armony, R., Polling Systems with Permanent and Transient Customers, Commun. Stat.: Stochastic Models, 1999, vol. 15, no. 3, pp. 395–427. · Zbl 0946.60085 · doi:10.1080/15326349908807543
[271] Ziouva, E. and Antonakopoulos, T., Improved IEEE 802.11 PCF Performance Using Silence Detection and Cyclic Shift on Stations Polling, IEE Proc. Commun., 2003, vol. 150, no. 1, pp. 45–51. · doi:10.1049/ip-com:20030139
[272] Ziouva, E. and Antonakopoulos, T., Efficient Voice Communications over IEEE802.11 WLANs Using Improved PCF Procedures, Proc. INC, Plymouth, 2002/2007.
[273] Ziouva, E. and Antonakopoulos, T., Improved IEEE802.11 PCF Performance Using Silence Detection and Cyclic Shift on Stations Polling, IEE Proc. Commun., 2003, vol. 150, no. 1, pp. 45–51. · doi:10.1049/ip-com:20030139
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