Abstract
We consider admission and routing controls for a system of N parallel tandem queues with finite buffers as N becomes large, with the aim of minimizing costs due to loss. We obtain the fluid limit as N→∞, and solve a related optimization problem. Asymptotically, for N large, the optimal cost and associated control take one of two forms, depending on the ratio between the cost of blocking an arrival at entry and discarding after service at the first queue.
Similar content being viewed by others
References
Arnott, R., Small, K.: The economics of traffic congestion. Am. Sci. 82, 446–455 (1994)
Boxma, O.J.: On a tandem queueing model with identical service times at both counters, I. Adv. Appl. Probab. 11, 616–643 (1979)
Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. Wiley, New York (1986)
Hillier, F.S., Boling, R.W.: Finite queues in series with exponential or Erlang service times—a numerical approach. Oper. Res. 15, 286–303 (1967)
Hordijk, A., Koole, G.: On the optimality of the generalized shortest queue policy. Probab. Eng. Inf. Sci. 4, 477–487 (1990)
Hordijk, A., Koole, G.: On the assignment of customers to parallel queues. Probab. Eng. Inf. Sci. 6, 495–511 (1992)
Hordijk, A., Koole, G.: On the shortest queue policy for the tandem parallel queue. Probab. Eng. Inf. Sci. 6, 63–79 (1992)
Hunt, P.J., Laws, C.N.: Least busy alternative routing in queueing and loss networks. Probab. Eng. Inf. Sci. 6, 439–456 (1992)
Hunt, P.J., Laws, C.N.: Asymptotically optimal loss network control. Math. Oper. Res. 18, 880–900 (1993)
Kelly, F.P.: The throughput of a series of buffers. Adv. Appl. Probab. 14, 633–653 (1982)
Koole, G.: On the static assignment to parallel servers. IEEE Trans. Autom. Control 44, 1588–1592 (1999)
Koole, G., Sparaggis, P.D., Towsley, D.: Minimizing response times and queue lengths in systems of parallel queues. J. Appl. Probab. 36, 1185–1193 (1999)
Laws, C.N., Teh, Y.C.: Alternative routing in fully-connected queueing networks. Adv. Appl. Probab. 32, 962–982 (2000)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)
Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49, 236–259 (2002)
Spicer, S., Ziedins, I.: User optimal state-dependent routing in parallel tandem queues with loss. J. Appl. Probab. 43, 274–281 (2006)
Tsoucas, P., Walrand, J.: On the interchangeability and stochastic ordering of ./M/1 queues in tandem. Adv. Appl. Probab. 19, 515–520 (1987)
Turner, S.R.E.: The effect of increasing routing choice on resource pooling. Probab. Eng. Inf. Sci. 12, 109–124 (1998)
Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: Queueing system with selection of the shortest of two queues: an asymptotic approach. Probl. Inf. Transm. 32, 15–27 (1996)
Whitt, W.: Some useful functions for functional limit theorems. Math. Oper. Res. 5, 67–85 (1980)
Whitt, W.: Deciding which queue to join: some counterexamples. Oper. Res. 34, 55–62 (1986)
Winston, W.: Optimality of the shortest line discipline. J. Appl. Probab. 14, 181–189 (1977)
Zhang, B., Ayhan, H.: Optimal admission control for tandem queues with loss. Preprint (2009)
Ziedins, I.: A paradox in a queueing network with state-dependent routing and loss. J. Appl. Math. Dec. Sci. 2007, 68280 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sheu, RS., Ziedins, I. Asymptotically optimal control of parallel tandem queues with loss. Queueing Syst 65, 211–227 (2010). https://doi.org/10.1007/s11134-010-9177-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11134-010-9177-y