In this study we analyze a queueing model with a Gurvich structure. In such a network, the controller may route incoming jobs to different classes, but they are routed to the same server. This structure, although it falls into the general class of stochastic processing networks, is somewhat unconventional. We focus on a single-server two-class version of a Gurvich network in this paper. For a Poisson arrival stream and exponential service rates, we develop a Markov decision process representation of the system and prove structural results on optimal routing and scheduling controls. We show that the optimal policy uses \(c\mu \) scheduling and switching curve routing. We also investigate the fluid model and perturbation expansions thereof, which are useful in deriving near-optimal policies in the original network.
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Ahn, H.S., Lewis, M.E.: Flexible server allocation and customer routing policies for two parallel queues when service rates are not additive. Oper. Res.
61(2), 344–358 (2013)
CrossRef
2.
Avram, F.: Optimal control of fluid limits of queuing networks and stochasticity corrections. Math. Stoch. Manuf. Syst.
33, 1–37 (1997)
3.
Bäuerle, N.: Asymptotic optimality of tracking policies in stochastic networks. Ann. Appl. Probab.
10(4), 1065–1083 (2000)
CrossRef
Cox, D.R., Smith, W.: Queues, Methuen & Co., Ltd, London, John Wiley & Sons, Inc., NY (1991)
6.
Gajrat, A., Hordijk, A., Ridder, A.: Large-deviations analysis of the fluid approximation for a controllable tandem queue. Ann. Appl. Probab.
13(4), 1423–1448 (2003)
CrossRef
7.
Kingman, J.: Two similar queues in parallel. Ann. Math. Stat.
32(4), 1314–1323 (1961)
CrossRef
8.
Lin, W., Kumar, P.R.: Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Autom. Control
29(8), 696–703 (1984)
CrossRef
9.
Maglaras, C.: Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality. Ann. Appl. Probab.
10(3), 897–929 (2000)
CrossRef
10.
Meyn, S.P.: Sequencing and routing in multiclass queueing networks. Part II: workload relaxations. SIAM J. Control Optim.
42(1), 178–217 (2003)
CrossRef
11.
Meyn, S.P.: Dynamic safety-stocks for asymptotic optimality in stochastic networks. Queueing Syst.
50(2–3), 255–297 (2005)
CrossRef
12.
Michael Harrison, J.: Brownian models of open processing networks: canonical representation of workload. Ann. Appl. Probab.
10(1), 75–103, 02 (2000)
CrossRef
Sennott, L.I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley Series in Probability and Statistics. Wiley, New York (1999)
15.
Sisbot, E.A.: Fluid and queueing networks with Gurvich-type routing. Ph.D. thesis, Graduate Program in Operations Research and Industrial Engineering, University of Texas at Austin (2015)
16.
Winston, W.: Optimality of the shortest line discipline. J. Appl. Probab.
14, 181–189 (1977)
CrossRef
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Titel
Joint routing and scheduling control in a two-class network with a flexible server
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