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Mean value analysis for polling systems. (English) Zbl 1137.90434
Summary: The present paper deals with the problem of calculating mean delays in polling systems with either exhaustive or gated service. We develop a mean value analysis (MVA) to compute these delay figures. The merits of MVA are in its intrinsic simplicity and its intuitively appealing derivation. As a consequence, MVA may be applied, both in an exact and approximate manner, to a large variety of models.

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
62H20 Measures of association (correlation, canonical correlation, etc.)
Full Text: DOI
[1] D. Bertsekas, R. Gallager, Data Networks (Prentice-Hall, New Jersey, 1987).
[2] O.J. Boxma, Workloads and waiting times in single-server systems with multiple customer classes (Queueing Systems, 5 (1989) 185–214). · Zbl 0681.60098
[3] R.B. Cooper, G. Murray, Queues served in cyclic order (The Bell System Technical Journal, 48 (1969) 675–689). · Zbl 0169.20804
[4] R.B. Cooper, Queues served in cyclic order: waiting times (The Bell System Technical Journal, 49 (1970) 399–413). · Zbl 0208.22502
[5] M. Eisenberg, Queues with periodic service and changeover time (Operations Research, 20 (2)(1972) 440–451). · Zbl 0245.60073 · doi:10.1287/opre.20.2.440
[6] M.J. Ferguson, Y. Aminetzah, Exact results for nonsymmetric token ring systems (IEEE Transactions on Communications, COM-33 (1985) 223–231).
[7] P. Franken, D. Koenig, W. Arndt, F. Schmidt, Queues and Point Processes (John Wiley, New York, 1982). · Zbl 0505.60058
[8] S.W. Fuhrmann, Performance analysis of a class of cyclic schedules (Bell Laboratories Technical Memorandum 81-59531-1, 1981).
[9] T. Hirayama, S.J. Hong, M. Krunz, A new approach to analysis of polling systems (Queueing Systems, 48 (1-2)(2004) 135–158). · Zbl 1061.60096 · doi:10.1023/B:QUES.0000039891.78286.dd
[10] A.G. Konheim, B. Meister, Waiting lines and times in a system with polling (Journal of the Association for Computing Machinery, 21 (3)(1974) 470–490). · Zbl 0298.68047
[11] A.G. Konheim, H. Levy, M.M. Srinivasan, Descendant set: an efficient approach for the analysis of polling systems (IEEE Transactions on Communications, 42 (2/3/4)(1994) 1245–1253). · doi:10.1109/TCOMM.1994.580233
[12] H. Levy, Delay computation and dynamic behavior of non-symmetric polling systems (Performance Evaluation, 10 (1) (1989) 35–51). · doi:10.1016/0166-5316(89)90004-7
[13] H. Levy, M. Sidi, Polling systems: applications, modeling and optimization (IEEE Transactions on Communications, COM-38 (10)(1990) 1750–1760). · doi:10.1109/26.61446
[14] J.D.C. Little, A proof of the queueing formula L = \(\lambda\) W (Operations Research, 9 (1961) 383–387). · Zbl 0108.14803
[15] C. Mack, T. Murphy, N.L. Webb, The efficiency of N machines uni-directionally patrolled by one operative when walking time and repair times are constants (Journal of the Royal Statistical Society Series B, 19 (1)(1957) 166–172). · Zbl 0090.35301
[16] C. Mack, The efficiency of N machines uni-directionally patrolled by one operative when walking time is constant and repair times are variable (Journal of the Royal Statistical Society Series B, 19 (1)(1957) 173–178). · Zbl 0090.35302
[17] J.A.C. Resing, Polling systems and multitype branching processes (Queueing Systems, 13 (1993) 409–426). · Zbl 0772.60069 · doi:10.1007/BF01149263
[18] I. Rubin, L.F.M. De Moraes, Message delay analysis for polling and token multiple-access schemes for local communication networks (IEEE Journal on Selected Areas in Communications, SAC-l (5)(1983) 935–947). · doi:10.1109/JSAC.1983.1145983
[19] D. Sarkar, W.I. Zangwill, Expected waiting time for nonsymmetric cyclic queueing systems–exact results and applications (Management Science, 35 (1989) 1463–1474). · Zbl 0684.90035 · doi:10.1287/mnsc.35.12.1463
[20] M.M. Srinivasan, H. Levy, A.G. Konheim, The individual station technique for the analysis of polling systems (Naval Research Logistics, 43 (1)(1996) 79–101). · Zbl 0862.60090 · doi:10.1002/(SICI)1520-6750(199602)43:1<79::AID-NAV5>3.0.CO;2-K
[21] G.B. Swartz, Polling in a loop system (Journal of the Association for Computing Machinery, 27 (1)(1980) 42–59). · Zbl 0438.94038
[22] H. Takagi, Queueing analysis of polling models: an update (In Stochastic Analysis of Computer and Communication Systems, H. Takagi (ed.), North-Holland, Amsterdam (1990) 267–318).
[23] H. Takagi, Queueing analysis of polling models: progress in 1990-1994 (In Frontiers in Queueing: Models, Methods and Problems, J.H. Dshalalow (ed.), CRC Press, Boca Raton (1997) 119–146). · Zbl 0871.60077
[24] H. Takagi, Analysis and application of polling models (In Performance Evaluation: Origins and Directions, G. Haring, C. Lindemann and M. Reiser (eds.), Lecture Notes in Computer Science, vol. 1769, Springer, Berlin (2000) 423–442).
[25] R.W. Wolff, Poisson arrivals see time averages (Operations Research, 30 (2) (1982) 223–231). · Zbl 0489.60096 · doi:10.1287/opre.30.2.223
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