×

Robustness of efficient server assignment policies to service time distributions in finite-buffered lines. (English) Zbl 1230.90065

Summary: We study the assignment of flexible servers to stations in tandem lines with service times that are not necessarily exponentially distributed. Our goal is to achieve optimal or near-optimal throughput. For systems with infinite buffers, it is already known that the effective assignment of flexible servers is robust to the service time distributions. We provide analytical results for small systems and numerical results for larger systems that support the same conclusion for tandem lines with finite buffers. In the process, we propose server assignment heuristics that perform well for systems with different service time distributions. Our research suggests that policies known to be optimal or near-optimal for Markovian systems are also likely to be effective when used to assign servers to tasks in non-Markovian systems.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahn, The optimal control of a two-stage tandem queueing system with flexible servers, Probability Eng Inform Sci 16 pp 453– (2002) · Zbl 1038.90018 · doi:10.1017/S0269964802164047
[2] Ahn, Optimal scheduling of a 2-stage tandem queue with parallel servers, Adv Appl Probability 31 pp 1095– (1999) · Zbl 0973.93061
[3] Ahn, Optimal control of a flexible server, Adv Appl Probability 36 pp 139– (2004) · Zbl 1072.93029
[4] Ahn, Dynamic load balancing with flexible workers, Adv Appl Probability 38 pp 621– (2006) · Zbl 1101.90034
[5] Andradóttir, Throughput maximization for tandem lines with two stations and flexible servers, Operat Res 53 pp 516– (2005) · Zbl 1165.90383
[6] Andradóttir, Server assignment policies for maximizing the steady-state throughput of finite queueing systems, Manage Sci 47 pp 1421– (2001) · Zbl 1232.90135
[7] Andradóttir, Dynamic server allocation for queueing networks with flexible servers, Operat Res 51 pp 952– (2003) · Zbl 1165.90384
[8] Andradóttir, Compensating for failures with flexible servers, Operat Res 55 pp 753– (2007) · Zbl 1167.90465
[9] Andradóttir, Dynamic assignment of dedicated and flexible servers in tandem lines, Probability Eng Inform Sci 21 pp 497– (2007) · Zbl 1145.90349 · doi:10.1017/S0269964807000290
[10] Andradóttir, Maximizing the throughput of tandem lines with flexible failure-prone servers and finite buffers, Probability Eng Inform Sci 22 pp 191– (2008) · Zbl 1171.90365 · doi:10.1017/S0269964808000119
[11] Bartholdi, A production line that balances itself, Operat Res 44 pp 21– (1996) · Zbl 0847.90063
[12] Bartholdi, Performance of bucket brigades when work is stochastic, Operat Res 49 pp 710– (2001) · Zbl 1163.90449
[13] Bell, Dynamic scheduling of a system with two parallel servers in heavy traffic with complete resource pooling: Asymptotic optimality of a continuous review threshold policy, Ann Appl Probability 11 pp 608– (2001) · Zbl 1015.60080
[14] Bell, Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: Asymptotic optimality of a threshold policy, Electron J Probability 10 pp 1044– (2005) · Zbl 1109.60075 · doi:10.1214/EJP.v10-281
[15] Bertsimas, Introduction to linear optimization (1997)
[16] Duenyas, Control of a single server queueing system with setups, Operat Res 46 pp 218– (1998) · Zbl 0979.90031
[17] Farrar, Optimal use of an extra server in a two station tandem queueing network, IEEE Trans Automatic Control 38 pp 1296– (1993) · Zbl 0825.93693
[18] Gel, Factors affecting opportunity of worksharing as a dynamic line balancing mechanism, IIE Trans 34 pp 847– (2002)
[19] Gurumurthi, Modeling and analysis of flexible queueing systems, Naval Res Logis 51 pp 755– (2004) · Zbl 1054.90017
[20] Hajek, Optimal control of two interacting service stations, IEEE Trans Automatic Control 29 pp 491– (1984) · Zbl 0555.90047
[21] Harrison, Heavy traffic resource pooling in parallel-server systems, Queueing Syst 33 pp 339– (1999) · Zbl 0997.60108
[22] Hillier, The effect of some design factors on the efficiency of production lines with variable operation times, J Ind Eng 17 pp 651– (1966)
[23] Hopp, Benefits of skill chaining in serial production lines with cross-trained workers, Manage Sci 50 pp 83– (2004)
[24] Hopp, Agile workforce evaluation: A framework for cross-training and coordination, IIE Trans 36 pp 919– (2004)
[25] Iravani, A robust policy for serial agile production systems, Naval Res Logist 52 pp 58– (2005) · Zbl 1140.90356
[26] Iravani, A twostage tandem queue attended by a moving server with holding and switching costs, Queueing Syst 26 pp 203– (1997) · Zbl 0892.90077
[27] Jordan, Principles on the benefits of manufacturing flexibility, Manage Sci 41 pp 577– (1995) · Zbl 0836.90087
[28] Kaufman, On the introduction of an agile, temporary workforce into a tandem queueing system, Queueing Syst 51 pp 135– (2005) · Zbl 1098.90021
[29] H.E. Kırkızlar Performance improvements through flexible workforce 2008
[30] Mandelbaum, Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized c{\(\mu\)}-rule, Operat Res 52 pp 836– (2004) · Zbl 1165.90402
[31] McClain, ”On-the-fly” line balancing with very little WIP, Int J Prod Econ 27 pp 283– (1992)
[32] Ostolaza, The use of dynamic (state-dependent) assembly-line balancing to improve throughput, J Manufacturing Operat Manage 3 pp 105– (1990)
[33] Rosberg, Optimal control of service in tandem queues, IEEE Trans Automatic Control 27 pp 600– (1982) · Zbl 0497.90024
[34] Sheikhzadeh, Machine sharing in manufacturing systems: Total flexibility versus chaining, Int J Flexible Manufacturing Syst 10 pp 351– (1998)
[35] Tassiulas, Allocation of interdependent resources for maximal throughput, Stochastic Models 16 pp 27– (2000) · Zbl 0978.90014
[36] Van Oyen, Performance opportunity for workforce agility in collaborative and noncollabortive work systems, IIE Trans 33 pp 761– (2001)
[37] Wallace, A staffing algorithm for call centers with skill-based routing, Manufacturing Service Operat Manage 7 pp 276– (2005)
[38] Williams, Analysis of communication networks: Call centres, traffic and performance 28, in: ”On dynamic scheduling of a parallel server system with complete resource pooling,” pp 49– (2000)
[39] Wu, Heuristics for allocation of reconfigurable resources in a serial line with reliability considerations, IIE Trans 40 pp 595– (2008)
[40] Wu, Dynamic allocation of reconfigurable resources in a two-stage tandem queueing system with reliability considerations, IEEE Trans Automatic Control 51 pp 309– (2006) · Zbl 1366.90085
[41] Zavadlav, Self-buffering, self-balancing, self-flushing production lines, Manage Sci 42 pp 1151– (1996) · Zbl 0880.90064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.