Abstract
We study a tandem queueing network with two stations, M heterogeneous flexible servers, and a finite intermediate buffer. The objective is to dynamically assign the servers to the stations in order to maximize the throughput of the system. The form of the optimal policy for M≤3 was derived in two previous papers. In one of those papers, Andradóttir and Ayhan (Operations Research 53:516–531, 2005) provide a conjecture on the form of the optimal policy for M≥4. We prove their conjecture in this paper, showing that the optimal policy is defined by monotone thresholds and the ratios of the service rates among the servers. For M>1, we also prove that the optimal policy always uses the entire intermediate buffer.
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Ahn, H.-S., Duenyas, I., Lewis, M.E.: The optimal control of a two-stage tandem queueing system with flexible servers. Probab. Eng. Inf. Sci. 16(4), 453–469 (2002)
Andradóttir, S., Ayhan, H.: Throughput maximization for tandem lines with two stations and flexible servers. Oper. Res. 53(3), 516–531 (2005)
Andradóttir, S., Ayhan, H., Down, D.: Server assignment policies for maximizing the steady-state throughput of finite queueing systems. Manag. Sci. 47(10), 1421–1439 (2001)
Andradóttir, S., Ayhan, H., Down, D.: Dynamic server allocation for queueing networks with flexible servers. Oper. Res. 51, 952–968 (2003)
Andradóttir, S., Ayhan, H., Down, D.: Compensating for failures with flexible servers. Oper. Res. 55, 753–768 (2007)
Andradóttir, S., Ayhan, H., Down, D.: Dynamic assignment of dedicated and flexible servers in tandem lines. Probab. Eng. Inf. Sci. 21, 497–538 (2007)
Andradóttir, S., Ayhan, H., Down, D.: Maximizing the throughput of tandem lines with flexible failure-prone servers and finite buffers. Probab. Eng. Inf. Sci. 22, 191–211 (2008)
Andradóttir, S., Ayhan, H., Down, D.: Queueing systems with synergistic servers. Oper. Res. (2011, to appear)
Bell, S.L., Williams, R.J.: 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. Probab. 11, 608–649 (2001)
Harrison, J.M., Lopez, M.J.: Heavy traffic resource pooling in parallel-server systems. Queueing Syst. 33, 339–368 (1999)
Kaufman, D., Ayn, H., Lewis, M.E.: On the introduction of an agile, temporary workforce into a tandem queueing system. Queueing Syst. 51(1–2), 135–171 (2005)
Kirkizlar, H.E., Andradóttir, S., Ayhan, H.: Flexible servers in understaffed tandem lines. Working paper (2010)
Mandelbaum, A., Stolyar, A.L.: Scheduling flexible servers with convex delay costs: heavy traffic optimality of the generalized cμ-rule. Oper. Res. 52, 836–855 (2004)
Puterman, M.L.: Markov Decision Processes. Wiley-Interscience, New York (1994)
Sennott, L.I., Van Oyen, M.P., Iravani, S.M.R.: Optimal dynamic assignment of a flexible worker on an open production line with specialists. Eur. J. Oper. Res. 170, 541–566 (2006)
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Hasenbein, J.J., Kim, B. Throughput maximization for two station tandem systems: a proof of the Andradóttir–Ayhan conjecture. Queueing Syst 67, 365–386 (2011). https://doi.org/10.1007/s11134-011-9222-5
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DOI: https://doi.org/10.1007/s11134-011-9222-5