Manufacturing flow line systems: A review of models and analytical results. (English) Zbl 0782.90048

Dallery, Yves; Gershwin, Stanley B.

Queueing Syst. 12, No. 1-2, 3-94 (1992).

Summary: The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features ( blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationship among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.

MSC:

90B30	Production models
90-02	Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming

Keywords:

manufacturing flow line; blocking; failures; repairs; quantitative measures of performance

References:

[1]	I. Adan and J. Wal, Monotonicity of the throughput in single server production and assembly networks with respect to the buffer sizes, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 345-356.
[2]	I.F. Akyildiz, On the exact and approximate throughput analysis of closed queueing networks with blocking, IEEE Trans. Soft. Eng. SE-14 (1988) 62-70. · doi:10.1109/32.4623
[3]	T. Altiok, Approximate analysis of exponential tandem queues with blocking, Europ. J. Oper. Res. 11 (1982). · Zbl 0497.60096
[4]	T. Altiok, On the phase-type approximations of general distributions, IIE Trans. 17 (1985) 110-116. · doi:10.1080/07408178508975280
[5]	T. Altiok, Production lines with phase-type operation and repair times and finite buffers, Int. J. Prod. Res. 23 (1985) 489-498. · Zbl 0571.90031 · doi:10.1080/00207548508904723
[6]	T. Altiok, Approximate analysis of queues in series with phase-type service times and blocking, Oper. Res. 37 (1989) 601-610. · Zbl 0674.90030 · doi:10.1287/opre.37.4.601
[7]	T. Altiok and R. Ranjan, Analysis of production lines with general service times and finite buffers: A two-node decomposition approach, Technical report, Department of Industrial and System Eng., Rutgers Univ. (1987).
[8]	T. Altiok and S. Stidham, Jr., A note on transfer lines with unreliable machines, random processing times, and finite buffers, IIE Trans. 14 (1982) 125-127.
[9]	T. Altiok and S. Stidham, Jr., The allocation of interstage buffer capacities in production lines, IIE Trans. 15 (1983) 292-299. · doi:10.1080/05695558308974650
[10]	R. Alvarez, Y. Dallery and R. David, An experimental study of the continuous flow model of transfer lines with unreliable machines and finite buffers, in:Modelling and Control of Technological Systems, IMACS (May 1991).
[11]	M.H. Ammar, Modelling and analysis of unreliable manufacturing assembly networks with finite storages, Technical Report LIDS-TH-1004, MIT Laboratory for Information and Decision Systems (1980).
[12]	M.H. Ammar and S.B. Gershwin, Equivalence relations in queueing models of fork/join queueing networks with blocking, Perf. Eval. 19 (1989) 233-245. · doi:10.1016/0166-5316(89)90013-8
[13]	B. Ancelin and A. Semery, Calcul de la productivité d’une ligne intégrée de fabrication: Calif, un logiciel basé sur une nouvelle heuristique, APII 21 (1987) 209-238.
[14]	D.R. Anderson, Transient and steady-state minimum cost in-process inventory capacities for production lines, PhD thesis, Dept. of Ind. Eng. Purdue University (1968).
[15]	G.T. Artamonov, Productivity of a two-instrument discrete processing line in the presence of failures, Cybernetics 12 (1977) 464-468.
[16]	B. Avi-Itzhak, A sequence of service stations with arbitrary and regular service times, Manag. Sci. 11 (1965) 565-571. · Zbl 0156.18602 · doi:10.1287/mnsc.11.5.565
[17]	P.G. Awate and B.L.N. Sastry, Analysis and decomposition of transfer and flow lines, Oper. Res. 24 (1987) 175-196. · Zbl 0629.90037
[18]	F. Baccelli, Ergodic theory of stochastic Petri networks (May 1989), to appear in Ann. Prob.
[19]	F. Baskett, Chandy, K.M., R.R. Muntz and F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers, J. ACM 22 (1975) 248-260. · Zbl 0313.68055 · doi:10.1145/321879.321887
[20]	O. Berman, Efficiency and production rate of a transfer line with two machines and a finite storage buffer, Europ. J. Oper. Res. 9 (1982) 295-308. · Zbl 0475.90035 · doi:10.1016/0377-2217(82)90038-8
[21]	A. Bobbio and K.S. Trivedi, Computation of the completion time when the work requirement is a PH random variable, in:Int. Conf. on Analysis and Control of Large Scale Stochastic Systems, Chapel Hill, NC (May 1988).
[22]	O.J. Boxma, Analysis of models for tandem queues, PhD thesis, University of Utrecht (1977).
[23]	D.E. Blumenfeld, A simple formula for estimating throughput of serial production likes with variable processing times and limited buffer capacity, Int. J. Prod. Res. 28 (1990) 1163-1182. · doi:10.1080/00207549008942783
[24]	G.M. Buxey, N.D. Slack and R. Wild, Production flow line system design ? a review, AIIE Trans. 5 (1973) 37-48.
[25]	J.A. Buzacott, Automatic transfer lines with buffer stocks, Int. J. Prod. Res. 5 (1967) 182-200. · doi:10.1080/00207546708929751
[26]	J.A. Buzacott, Markov chain analysis of automatic transfer line with buffer stock, PhD thesis, Dept. of Eng. Prod., Univ. of Birmingham (1967).
[27]	J.A. Buzacott, Prediction of the efficiency of production systems without internal storage, Int. J. Prod. Res. 6 (1968) 173-188. · doi:10.1080/00207546708929778
[28]	J.A. Buzacott, Methods of reliability analysis of production systems subject to breakdowns, in:Operations Research and Reliability, ed. D. Grouchko, Turin, Italy (1969) pp. 211-232.
[29]	J.A. Buzacott, The effect of station breakdowns and random processing times on the capacity of flow lines, AIIE Trans. 4 (1972) 308-312.
[30]	J.A. Buzacott, Optimal operating rules for automatic manufacturing systems, IEEE Trans. Auto. Control AC-27 (1982) 80-86. · doi:10.1109/TAC.1982.1102820
[31]	J.A. Buzacott, Abandoning the moving assembly line: Models of human operators and job sequencing, Int. J. Prod. Res. 28 (1990) 821-839. · doi:10.1080/00207549008942758
[32]	J.A. Buzacott and L.E. Hanifin, Models of automatic transfer lines with inventory banks ? a review and comparison, IIE Trans. 10 (1978) 197-207. · doi:10.1080/05695557808975204
[33]	J.A. Buzacott and L.E. Hanifin, Transfer line design and analysis ? an overview, in:IIE Conf. (1978).
[34]	J.A. Buzacott and D. Kostelski, Matrix-geometric and recursive algorithm solution of a two-stage unreliable flow line, IIE Trans. 19 (1987) 429-438. · doi:10.1080/07408178708975416
[35]	M. Caramanis, Production system design: A discrete event dynamic system and generalized Benders’ decomposition approach, Int. J. Prod. 25 (1987) 1223-1234. · Zbl 0623.90032
[36]	Y.F. Choong and S.B. Gershwin, A decomposition method for the approximate evaluation of capacitated transfer lines with unreliable machines and random processing times, IIE Trans. 19 (1987) 150-159. · doi:10.1080/07408178708975381
[37]	J.W. Cohen,The Single Server Queue (North-Holland, Amsterdam, 1982).
[38]	P. Coillard and J.-M. Proth, Sur l’effet des stocks tampons dans use fabrication en ligne, Rev. Belge Statist. Inform. et Recherche Oper. 24 (1984) 3-27. · Zbl 0544.90054
[39]	C. Commault and Y. Dallery, Production rate of transfer lines with no intermediate storage, IIE Trans. 22 (1990) 315-329. · doi:10.1080/07408179008964186
[40]	C. Commault and A. Semery, Taking into account delays in buffers for analytical performance evaluation of transfer lines, IIE Trans. 22 (1990) 133-142. · doi:10.1080/07408179008964165
[41]	Y. Dallery, R. David and X.-L. Xie, An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers, IIE Trans. 20 (1988) 280-283. · doi:10.1080/07408178808966181
[42]	Y. Dallery, R. David and X.-L. Xie, Approximate analysis of transfer lines with unreliable machines and finite buffers, IEEE Trans. Auto. Control AC-34 (1989) 943-953. · Zbl 0689.68118 · doi:10.1109/9.35807
[43]	Y. Dallery and Y. Frein, A decomposition method for approximate analysis of closed queueing networks with blocking, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 193-216.
[44]	Y. Dallery and Y. Frein, On decomposition methods for tandem queueing networks with blocking, MASI technical report, Université Pierre et Marie Curie, Paris, France (1989), to appear in Oper. Res. · Zbl 0771.90046
[45]	Y. Dallery, Z. Liu and D. Towsley, Equivalence, reversibility, and symmetry properties in fork/join queueing networks with blocking, Technical report MASI, No. 90-23, Univ. Pierre et Marie Curie, Paris, France (1990).
[46]	Y. Dallery, Z. Liu and D. Towsley, Properties of fork/join queueing networks with blocking under various operating mechanisms, Technical Report COINS, University of Massachusetts at Amherst (1992).
[47]	Y. Dallery and D. Towsley, Symmetry property of the throughout in closed tandem queueing networks with finite buffers, Oper. Res. Lett. 10 (1991) 541-547. · Zbl 0744.60106 · doi:10.1016/0167-6377(91)90075-Z
[48]	E.S. Dattatreya, Tandem queueing systems with blocking, PhD Thesis, Dept. of Ind. Eng. and Op. Res., Univ. of California, Berkeley (1978).
[49]	R. David, A. Semery, B. Ancelin and C. Terracol, Evaluation des performances d’une ligne de production par des méthodes d’agrégation, in:INRIA 2nd Int. Conf. on Production Systems (1987).
[50]	R. David, X.-L. Xie and Y. Dallery, Properties of continuous models of transfer lines with unreliable machines and finite buffers, IMA J. Math. Bus. Ind. 6 (1990) 281-308. · Zbl 0718.90040
[51]	A.G. De Kok, Computationally efficient approximations for balanced flowlines with finite intermediate storage, Technical report, Philips Centre for Quantitative Methods Report CQM-Note 073 (1988). · Zbl 0684.90047
[52]	M.B.M. De Koster, Approximation of assembly-disassembly systems, Technical report BDK/ORS/87-02, Dept. of Ind. Eng., Eindhoven Univ. of Technology, Eindhoven, The Netherlands (1987).
[53]	M.B.M. De Koster, Estimation of line efficiency by aggregation, Int. J. Prod. Res. 25 (1987) 615-626. · doi:10.1080/00207548708919865
[54]	M.B.M. De Koster, Capacity oriented analysis and design of production systems, PhD thesis, Eindhoven Univ. of Technology, Eindhoven, The Netherlands (1988). · Zbl 0724.90018
[55]	M.B.M. De Koster, An improved algorithm to approximate behaviour of flow lines, Int. J. Prod. Res. 26 (1988) 691-700. · doi:10.1080/00207548808947892
[56]	M.B.M. De Koster and J. Wijngaard, Continuous vs. discrete models for production lines with blocking, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 175-192.
[57]	M. Di Mascolo, R. David and Y. Dallery, Modelling and analysis of assembly systems with unreliable machines and finite buffers, IIE Trans. 23 (1991) 315-330. · doi:10.1080/07408179108963866
[58]	M. Di Mascolo, Y. Frein, Y. Dallery and R. David, A unified modeling of kanban systems using Petri nets, Int. J. Flexible Manufacturing Syst. 3 (1991) 275-307.
[59]	D. Dubois and J.-P. Forestier, Productivité et en cours moyen d’un ensemble de deux machines séparées par une zone de stockage, RAIRO Automatique 16 (1982) 105-132. · Zbl 0486.90048
[60]	A. Dudick, Fixed cycle production systems with in-line inventory and limited repair capability, PhD thesis, Columbia University, New York (1979).
[61]	E.A. Elsayed and Hwang, Analysis of manufacturing systems with buffer storage and redundant machines, IE working paper, Dept. of Ind. Eng., Rutgers Univ. (1984).
[62]	E.A. Elsayed and R.E. Turley, Reliability analysis of production systems with buffer storage, Int. J. Prod. Res. 18 (1980).
[63]	Y.B. Erpsher, Losses of working time and division of automatic lines into sections, Stanki i Instrument 23 (1952) 7-16 [English transl.: DSIR CTS 631 and CTS 634].
[64]	M.P. Fanti, B. Maione, R. Peluso and B. Turchiano, Large Markov chain modelling and analysis of transfer lines with unreliable work stations and finite buffers, Working paper, Dip. di Elettrotecnica ed Ellectronica, Univ. di Bari, Italy (1987). · Zbl 0673.90037
[65]	J.-P. Forestier, Modélisation stochastique et comportement asymptotique d’un système automatisé de production, RAIRO Automatique 14 (1980) 127-144. · Zbl 0442.90033
[66]	Y. Frein, C. Commault and Y. Dallery, Analytical performance evaluation of closed transfer lines with limited number of pallets, in:IEEE Conf. on Robotics and Automation (1992).
[67]	Y. Frein and Y. Dallery, Analysis of cyclic queueing networks with finite buffers and service blocking, Perf. Eval. 10 (1989) 197-210. · doi:10.1016/0166-5316(89)90010-2
[68]	D.P. Gaver, A waiting line with interrupted service, including priorities, J. Roy. Stat. Soc, B24 (1954) 73-90. · Zbl 0108.31403
[69]	S.B. Gershwin, Assembly/disassembly systems: An efficient decomposition algorithm for tree-structured networks, Technical Report LIDS-P-1579, MIT Laboratory for Information and Decision Systems (1986).
[70]	S.B. Gershwin, An efficient decomposition algorithm for the approximate evaluation of tandem queues with finite storage space and blocking, Oper. Res. 35 (1987) 291-305. · Zbl 0626.90027 · doi:10.1287/opre.35.2.291
[71]	S.B. Gershwin, Representation analysis of transfer lines with machines that have different processing rates, Ann. Oper. Res. 9 (1987) 511-530. · doi:10.1007/BF02054752
[72]	S.B. Gershwin, An efficient decomposition algorithm for unreliable tandem queueing systems with finite buffers, in:Queueing Networks with blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 127-146.
[73]	S.B. Gershwin,Manufacturing Systems Engineering (Prentice-Hall, 1993).
[74]	S.B. Gershwin, Assembly/disassembly systems: An efficient decomposition algorithm for tree-structured networks, IIE Trans. 23 (1993).
[75]	S.B. Gershwin and O. Berman, Analysis of transfer lines consisting of two unreliable machines with random processing times and finite storage buffers, AIIE Trans. 13 (1981).
[76]	S.B. Gershwin and I.C. Schick, Continuous model of an unreliable two-stage material flow system with a finite interstage buffer, Technical Report LIDS-R-1039, MIT Laboratory for Information and Decision Systems (1980).
[77]	S.B. Gershwin and I.C. Schick, Modelling and analysis of three-stage transfer lines with unreliable machines and finite buffers, Oper. Res. 31 (1983) 354-380. · Zbl 0507.90042 · doi:10.1287/opre.31.2.354
[78]	C.R. Glassey and Y. Hong, The analysis of behavior of an unreliablen-stage automatic transfer line with (n ?1) inter-stage buffer storages, Technical report, Dept. of Ind. Eng. and Oper. Res., University of California, Berkeley (1986).
[79]	C.R. Glassey and Y. Hong, The analysis of behavior of an unreliable two-stage automatic transfer line with inter-stage buffer storage, Technical report, Dept. of Ind. Eng. and Oper. Res., Univ. of California, Berkeley (1986).
[80]	W.J. Gordon and G.F. Newell, Cyclic queueing systems with restricted length queues, Oper. Res. 15 (1967) 266-277. · Zbl 0168.16604 · doi:10.1287/opre.15.2.266
[81]	L. Gun, Tandem queueing systems subject to blocking with phase-type servers: Analytic solutions and approximations, Master’s thesis, Dept. of Elec. Eng., Univ. of Maryland, College Park (1987).
[82]	L. Gun and A.M. Makowski, Matrix-geometric solution for finite capacity queues with phase-type distributions, in:Performance ’87 (1987).
[83]	L. Gun and A.M. Makowski, Matrix-geometric solution for two-node tandem queueing systems with phase-type servers subject to blocking and failures (1987).
[84]	L. Gun and A.M. Makowski, An approximation method for general tandem queueing systems subject to blocking, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 147-174.
[85]	B.J. Haydon, The behavior of systems of finite queues, PhD thesis, Univ. of New South Wales, Kensington (1973). · Zbl 0277.46054
[86]	U. Herzog, R. Woo and K.M. Chandy, Solution of queueing problems by a recursive technique, IBM J. Res. Develop. 19 (1975) 295-300. · Zbl 0307.68043 · doi:10.1147/rd.193.0295
[87]	D.K. Hildebrand, Stability of finite queue, tandem server systems, J. Appl. Prob. 4 (1967) 571-583. · Zbl 0157.25302 · doi:10.2307/3212222
[88]	D.K. Hildebrand, On the capacity of tandem server, finite queue, service systems, Oper. Res. 16 (1968) 72-82. · Zbl 0157.25401 · doi:10.1287/opre.16.1.72
[89]	F.S. Hillier and R.W. Boling, The effect of some design factors on the efficiency of production lines with variable operation times, J. Ind. Eng. 17 (1966) 651-658.
[90]	F.S. Hillier and R.W. Boling, Finite queues in series with exponential or erlang service times ? a numerical approach, Oper. Res. 16 (1967) 286-303. · Zbl 0171.16302 · doi:10.1287/opre.15.2.286
[91]	F.S. Hillier and R.W. Boling, Optimal allocation of work in production line systems with variable operation times, Oper. Res. technical report 33, Dept. of Oper. Res., Stanford University (1972). · Zbl 0369.90051
[92]	F.S. Hillier and R.W. Boling, Toward characterizing the optimal allocation of work in production lines with variable operation times, in:Advances in Operations Research, ed. M. Reubens (North-Holland, Amsterdam, 1977). · Zbl 0369.90051
[93]	F.S. Hillier and R.W. Boling, On the optimal allocation of work in symmetrically unbalanced production line systems with variable operation times, Manag. Sci. 25 (1979) 721-728. · doi:10.1287/mnsc.25.8.721
[94]	Y.C. Ho, M.A. Eyler and T.T. Chien, A gradient technique for general buffer storage design in a production line, Int. J. Prod. Res. 17 (1979) 557-580. · Zbl 0427.90047 · doi:10.1080/00207547908919637
[95]	Y. Hong and D. Seong, The analysis of an unreliablen-machine flow-line manufacturing system with random processing times, Technical report No. 89-03, Dept. of Ind. Eng., Pohang Institute of Technology (1989).
[96]	G.C. Hunt, Sequential arrays of waiting lines, Oper. Res. 4 (1956) 674-683. · doi:10.1287/opre.4.6.674
[97]	E. Ignall and A. Silver, The output of a two-stage system with unreliable machines and limited storage, AIIE Trans. 9 (1977) 183-188.
[98]	T. Iyama and S. Ito, The maximum production rate for an unbalanced multi-server flow line system with finite buffer storage, Int. J. Prod. Res. 25 (1987) 1157-1170. · Zbl 0625.90040
[99]	M. Jafari and J.G. Shanthikumar, An approximate model of multistage automatic transfer lines with possible scrapping of workpieces, IIE Trans. 19 (1987) 252-265. · doi:10.1080/07408178708975394
[100]	M. Jafari and J.G. Shanthikumar, Exact and approximate solutions to two-stage transfer lines with general uptime and downtime distributions, IIE Trans. 19 (1987) 412-420. · doi:10.1080/07408178708975414
[101]	K.P. Jun and H.G. Perros, An approximate analysis of open tandem queueing networks with blocking and general service times, Computer Science report 87-17, North Carolina University (1987).
[102]	L. Kleinrock,Queueing Systems, vol. 1 (Wiley, 1975). · Zbl 0334.60045
[103]	A.D. Knott, The efficiency of series production lines, PhD thesis, University of New South Wales (1967).
[104]	A.D. Knott, The inefficiency of a series of work stations ? a simple formula, Int. J. Prod. Res. 8 (1970) 109-119. · doi:10.1080/00207547008929834
[105]	E. Koenisberg, Production lines and internal storage ? a review, Manag. Sci. 5 (1959) 410-433. · doi:10.1287/mnsc.5.4.410
[106]	H.-S. Lau, A directly-coupled two-stage unpaced line, IIE Trans. 18 (1986) 304-312. · doi:10.1080/07408178608974708
[107]	H.-S. Lau, The production rate of a two-stage system with stochastic processing times, Int. J. Prod. Res. 24 (1986) 401-412. · Zbl 0584.90039 · doi:10.1080/00207548608919737
[108]	S.S. Lavenberg, The steady-state queueing time distribution for theM/G/1 finite capacity queue, Manag. Sci. 21 (1975) 501-506. · Zbl 0302.60058 · doi:10.1287/mnsc.21.5.501
[109]	J.-T. Lim and S.M. Meerkov, Analysis and synthesis of asymptotically reliable closed serial production lines, in:IEEE Conf. on Decision and Control, Hawaii (December 1990).
[110]	J.-T. Lim, S.M. Meerkov and F. Top, Homogeneous, asymptotically reliable serial production lines: Theory and a case study, IEEE Trans. Auto. Control AC-35 (1990). · Zbl 0715.90061
[111]	J.D.C. Little, A proof of the queueing formulaL=?W, Oper. Res. 9 (1961) 383-387. · Zbl 0108.14803 · doi:10.1287/opre.9.3.383
[112]	X.-G. Liu, Toward modeling assembly systems: applications of queueing networks with blocking, PhD thesis, Dept. of Management Sciences. Univ. of Waterloo, Waterloo (1990).
[113]	X.-G. Liu and J.A. Buzacott, A zero-buffer equivalence technique for decomposing queueing networks with blocking, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 87-104.
[114]	X.-G. Liu and J.A. Buzacott, Approximate models of assembly systems with finite inventory banks, Europ. J. Oper. Res. 45 (1990) 143-154. · Zbl 0707.90040 · doi:10.1016/0377-2217(90)90181-A
[115]	R. Marie, Calculating equilibrium probabilities for ?(n)/Ck/1/N queues, in:Performance’ 80 (1980) pp. 117-125.
[116]	B. Melamed, A note on the reversibility and duality of some tandem blocking queueing systems, Manag. Sci. 32 (1986) 1648-1650. · Zbl 0621.60105 · doi:10.1287/mnsc.32.12.1648
[117]	G.J. Miltenburg, Variance of the number of units produced on a transfer line with buffer inventories during a period of lengtht, Naval Res. Logistics 34 (1987) 811-822. · Zbl 0648.90034 · doi:10.1002/1520-6750(198712)34:6<811::AID-NAV3220340606>3.0.CO;2-Z
[118]	D. Mitra, Stochastic theory of a fluid model of multiple failure-susceptible producers and consumers coupled by a buffer, Advan. Appl. Prob. (September, 1988). · Zbl 0656.60079
[119]	E.J. Muth, The production rate of a series of work stations with variable service times, Int. J. Prod. Res. 11 (1973) 155-169. · doi:10.1080/00207547308929957
[120]	E.J. Muth, Numerical methods applicable to a production line, in:Algorithmic Methods in Probability, ed. M.F. Neuts, TIMS Studies in the Management Sciences (North-Holland, Amsterdam, 1977) pp. 143-160.
[121]	E.J. Muth, The reversibility property of production lines, Manag. Sci. 25 (1979) 152-158. · Zbl 0419.90044 · doi:10.1287/mnsc.25.2.152
[122]	E.J. Muth, Stochastic processes and their network representations associated with a production line queueing model, Oper. Res. 15 (1984) 63-83. · Zbl 0525.90057 · doi:10.1016/0377-2217(84)90049-3
[123]	E.J. Muth, An update on analytic models of serial transfer lines, Research report No. 87-15, Dept. of Ind. and Syst. Eng., Univ. of Florida, Gainesville, FL (1987).
[124]	E.J. Muth and A. Alkaff, The throughput rate of three-station production lines: A unifying solution, Int. J. Prod. Res. 25 (1987) 1405-1413. · Zbl 0623.90031 · doi:10.1080/00207548708919831
[125]	M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (The Johns Hopkins Univ. Press, 1981). · Zbl 0469.60002
[126]	V.F. Nicola, A single server queue with mixed types of interruptions, Acta Inform. 23 (1986) 465-486. · Zbl 0569.60095 · doi:10.1007/BF00267867
[127]	K. Okamura and H. Yamashina, Analysis of the effect of buffer storage capacity in transfer line systems, AIIE Trans. 9 (1977) 127-135.
[128]	R. Onvural, A survey of closed queueing networks with finite buffers, ACM Comput. Surveys 22 (1991) 83-121. · doi:10.1145/78919.78920
[129]	R. Onvural and H.G. Perros, On equivalencies of blocking mechanism in queueing networks with blocking, Oper. Res. Lett. 5-6 (1986) 293-298. · Zbl 0616.60093 · doi:10.1016/0167-6377(86)90067-2
[130]	R. Onvural and H.G. Perros, Throughput analysis of cyclic queueing networks with blocking, Technical report, CS Dept., North Carolina State University, Raleigh (1987). · Zbl 0616.60093
[131]	R. Onvural and H.G. Perros, Some equivalencies between open and closed queueing networks with finite buffers, Perf. Eval. 9 (1989) 111-118. · Zbl 0661.60109 · doi:10.1016/0166-5316(89)90036-9
[132]	R. Onvural, H.G. Perros and T. Altiok, On the complexity of the matrix-geometric solution of exponential open queueing networks with blocking, in:Int. Workshop in Modelling Techniques and Performance Evaluation, eds. Pujolle et al. (North-Holland, Amsterdam, 1987).
[133]	J. Ou and S.B. Gershwin, The variance of the lead time distribution of a two-machine transfer line with a finite buffer, Technical Report LMP-89-028, MIT Laboratory for Manufacturing and Productivity (1989).
[134]	H.G. Perros, Queueing networks with blocking: A bibliography, Perf Eval. Rev. 12 (1986) 8-14. · doi:10.1145/1041823.1041824
[135]	H.G. Perros, A survey of two-node queueing networks with blocking, Technical report 88-06, CS Dept., North Carolina State University, Raleigh (1988).
[136]	H.G. Perros, Stochastic analysis of computer and communication systems, in:Open Queueing Networks with Blocking, ed. H. Takagi (North-Holland, Amsterdam, 1989).
[137]	H.G. Perros and T. Altiok, Approximate analysis of open networks of queues with blocking: Tandem configurations, IEEE Trans. Software Eng. SE-12 (1986) 450-461.
[138]	H.G. Perros and T. Altiok (eds.),1st Int. Workshop on Queueing Networks with Blocking, Raleigh, North Carolina (Elsevier, 1989).
[139]	B. Philippe, Y. Saad and W.J. Stewart, Numerical methods in markov modeling, Technical Report No. 495, INRIA (September 1989). · Zbl 0764.65095
[140]	J.-J. Pierrat, Modélisation de systèmes a événements discrets sujets à des pannes, PhD thesis, Laboratoire d’Automatique de Grenoble, Institut National Polytechnique de Grenoble, Grenoble (1987).
[141]	S.M. Pollock, J.R. Birge and J.M. Alden, Approximation analysis for open tandem queues with blocking, IE report 85-30, University of Michigan (1985).
[142]	N.P. Rao, On the mean production of a two-stage production system of the tandem type, Int. J. Prod. Res. 13 (1975) 207-217. · doi:10.1080/00207547508942987
[143]	N.P. Rao, Two-stage production systems with intermediate storage, AIIE Trans. 7 (1975) 414-421.
[144]	N.P. Rao, A generalization of the bowl phenomenon in series production systems, Int. J. Prod. Res. 14 (1976) 437-443. · doi:10.1080/00207547608956617
[145]	N.P. Rao, A viable alternative to the method of stages solution of series production systems with Erlang service times, Int. J. Prod. Res. 14 (1976) 699-702. · doi:10.1080/00207547608956388
[146]	B.L.N. Sastry, Analysis of two-machine Markovian production lines and decomposition of longer lines, PhD thesis, Ind. Eng. and Oper. Res. Group, Indian Institute of Technology, Bombay (1985).
[147]	B.L.N. Sastry and P.G. Awate, Analysis of a two station flow-line with machine processing subject to inspection and rework, Opsearch 25 (1988) 89-97. · Zbl 0654.90032
[148]	C.H. Sauer and K.M. Chandy,Computer Systems Performance Modeling (Prentice-Hall, 1981).
[149]	I.C. Schick and S.B. Gershwin, Modelling and analysis of unreliable transfer lines with finite interstage buffers, Electronic systems laboratory report ESL-FR-834-6, Massachusetts Inst. of Technology (1978).
[150]	P.J. Schweitzer and T. Altiok, Aggregate modelling of tandem queues without intermediate buffers, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 47-72.
[151]	A. Semery, Modélisation des LIF: Intégration du modèle de Dubois et Forestier à l’heuristique de Gershwin, pour les lignes à temps de cycle différents, Rapport de recherche AS/619-87, Regie Renault, Direction de la Recherche (1987).
[152]	A. Semery, Modélisation des LIF: Comportement et limites des modèles basés sur la méthode de decomposition de Gershwin, Rapport de recherche AS/619/87, Régie Renault, Direction de la Recherche (April 1988).
[153]	B.A. Sevast’yanov, Influence of storage bin capacity on the average standstill time of a production line, Teoriya Veroyatnostey i ee Primeneniya 7 (1962) 438-447 [Eng. transi.: Theory Prob. Appl. 7 (1962) 429-438].
[154]	J.G. Shanthikumar and M.A. Jafari, Bounding the performance of tandem queues with finite buffer spaces, Working paper, University of California at Berkeley (October 1987). · Zbl 0787.60118
[155]	J.G. Shanthikumar and D.D. Yao, Monotonicity and concavity properties in cyclic queueing networks with finite buffers, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (North-Holland, Amsterdam, 1989) pp. 325-345.
[156]	J.G. Shanthikumar and C.C. Tien, An algorithmic solution to two-stage transfer lines with possible scrapping of units, Manag. Sci. 29 (1983) 1069-1086. · Zbl 0522.90043 · doi:10.1287/mnsc.29.9.1069
[157]	T.J. Sheskin, Allocation of interstage storage along an automatic transfer production line with discrete flow, PhD thesis, Dept. of Ind. and Management Engineering, Pennsylvania State University (1974).
[158]	T.J. Sheskin, Allocation of interstage storage along and automatic production line, AIIE Trans. 8 (1976) 146-152.
[159]	T.L. Smunt and W.C. Perkins, Stochastic unpaced line design: Review and further experimental results, J. Oper. Manag. 5 (1985) 351-373. · doi:10.1016/0272-6963(85)90019-1
[160]	A.L. Soyster, J.W. Schmidt and M.W. Rohrer, Allocations of buffer capacities for a class of fixed cycle production systems, AIIE Trans. 11 (1979).
[161]	A.L. Soyster and D.I. Toof, Some comparative and design aspects of fixed cycle production systems, Naval Res. Logistics Quarterly 23 (1976) 437-454. · Zbl 0394.90046 · doi:10.1002/nav.3800230306
[162]	W.J. Stewart, Numerical solution of markov chains: Block Hessenberg matrices and solution by recursion, Technical report no. 88-29, Dept. of Computer Science, North Carolina State University (1988).
[163]	W.J. Stewart, A comparison of numerical techniques in Markov modeling, Commun. ACM 21 (1978) 144-152. · Zbl 0383.65067 · doi:10.1145/359340.359350
[164]	R. Suri and G. Diehl, A new building block for performance evaluation of queueing networks with finite buffers, in:Conf. on Measurement and Modeling of Computer Systems (ACM Sigmetrics, 1984) pp. 134-142.
[165]	R. Suri and G. Diehl, A variable buffer-size model and its use in analyzing closed queueing networks with blocking, Manag. Sci. 32 (1986) 206-224. · Zbl 0587.60091 · doi:10.1287/mnsc.32.2.206
[166]	Y. Takahashi, H. Miyahara and T. Hasegawa, An approximation method for open restricted queueing networks, Oper. Res. 28 (1980). · Zbl 0442.90025
[167]	C. Terracol and R. David, An aggregation method for performance evaluation of transfer lines with unreliable machines and finite buffers, in:Int. Conf. on Robotics and Automation, Raleigh, NC (IEEE, 1987).
[168]	C. Terracol and R. David, Performances d’une ligne composée de machines et de stock intermédiaires, APII 21 (1987) 239-262.
[169]	F. Top, Asymptotic analysis and synthesis of serial production systems, PhD thesis, Univ. of Michigan (1990).
[170]	N.M. Van Dijk and B.F. Lamond, Simple bounds for finite single-server exponential tandem queues, Oper. Res. 36 (1988) 470-477. · Zbl 0646.60102 · doi:10.1287/opre.36.3.470
[171]	A.P. Vladzievskii, Probabilistic law of operation and internal storage of automatic lines, Avtomatika i Telemehanika 13 (1952) 227-281 (in Russian).
[172]	A.P. Vladzievskii, Losses of working time and the division of automatic lines into sections, Stanki i Instrument 24 (1953) (in Russian) [Eng. transi.: DSIR CTS 632].
[173]	J. Wijngaard, The effect of interstage buffer storage on the output of two unreliable production units in series with different production rates, AIIE Trans. 11 (1979) 42-47.
[174]	R.P. Wiley, Analysis of a tandem queue model of a transfer line, Laboratory for Information and Decision Systems Report LIDS-P-1150, Massachusetts Institute of Technology, Cambridge (September 1981).
[175]	X.-L. Xie, An efficient algorithm for performance analysis of transfer lines and its convergence, Working paper, INRIA-Lorraine, France (1989).
[176]	G. Yamazaki, T. Kawashima and H. Sakasegawa, Reversibility of tandem blocking queueing systems, Planag. Sci. 31 (1985) 78-83. · Zbl 0609.90046
[177]	G. Yamazaki and H. Sakasegawa, Properties of duality in tandem queueing systems, Ann. Inst. Statist. Math. 27 (1975) 201-212. · Zbl 0374.60125 · doi:10.1007/BF02504640
[178]	S. Yeralan and E.J. Muth, A general model of a production line with intermediate buffer and station breakdown, IIE Trans. 19 (1987) 130-139. · doi:10.1080/07408178708975379
[179]	I.Yu Retsker and A.A. Bunin, Determining the main parameters of transfer lines, Stanki i Instrument 35 (1964) 6-17.
[180]	B. Zimmern, Etudes de la propagation des arrêts aléatoires dans les chaines de production, Rev. Statist. Appl. 4 (1956) 85-104.
[181]	A. Brandwajn and Y.L. Jow, An approximation method for tandem queues with blocking, Oper. Res. 36 (1988) 73-83. · Zbl 0643.90026 · doi:10.1287/opre.36.1.73