Abstract
We give a closed-form expression for the discounted weighted queue length and switching costs of a two-class single-server queueing model under a preemptive priority rule. These expressions are used to do a single step of policy iteration in a polling model with a dynamically controlled switching rule, starting from the preemptive priority rule. Numerical experiments show that this leads to a policy that performs well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.S. Baras, D.-M. Ma and A.M. Makowski, K competing queues with geometric requirements and linear costs: The μc-rule is always optimal, Systems Control Lett. 6 (1985) 173–180.
D.P. Bertsekas and J.N. Tsitsiklis, Neuro-Dynamic Programming (Athena Scientific, 1996).
C. Buyukkoc, P. Varaiya and J. Walrand, The cμ rule revisited, Adv. in Appl. Probab. 17 (1985) 237–238.
R.-R. Chen and S. Meyn, Value iteration and optimization of multiclass queueing networks, Queueing Systems 32 (1999) 65–97.
J.M. Harrison, A priority queue with discounted linear costs, Oper. Res. 23 (1975) 260–269.
N.K. Jaiswal, Priority Queues (Academic Press, New York, 1968).
G.M. Koole, Assigning a single server to inhomogeneous queues with switching costs, Theoret. Comput. Sci. 182 (1997) 203–216.
G.M. Koole, The deviation matrix of the M/M/1∞ and M/M/1N queue, with applications to controlled queueing models, in: Proc. of the 37th IEEE Conf. on Decision and Control (1998) pp. 56–59.
P. Nain and D. Towsley, Optimal scheduling in a machine with stochastic varying processing rate, IEEE Trans. Automat. Control 39 (1994) 1853–1855.
T.J. Ott and K.R. Krishnan, Separable routing: A scheme for state-dependent routing of circuit switched telephone traffic, Ann. Oper. Res. 35 (1992) 43–68.
M.L. Puterman, Markov Decision Processes (Wiley, New York, 1994).
S.A.E. Sassen, H.C. Tijms and R.D. Nobel, A heuristic rule for routing customers to parallel servers, Statistica Neerlandica 51 (1997) 107–121.
H. Takagi, Analysis of Polling Systems (MIT Press, Cambridge, MA, 1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koole, G., Nain, P. On the value function of a priority queue with an application to a controlled polling model. Queueing Systems 34, 199–214 (2000). https://doi.org/10.1023/A:1019109103725
Issue Date:
DOI: https://doi.org/10.1023/A:1019109103725