Abstract
In this paper we deal with two stationary loss queuing network location models. We analyze the influence of filtering policies on the locational aspect of the problems. We assume that requests for service are placed at nodes of a transportation network and they arrive in time as independent homogeneous Poisson processes with different input rates. The considered policies only cover a given proportion of requests even if there are idle service units. This proportion is stationary and fixed in advance and only depends on the node where the request is originated. The objective is to find the location of the facilities together with the filtering policy to be applied that minimize the expected total cost per unit time with respect to a given cost structure. Properties and computational results are presented enabling the resolution of these problems efficiently and showing the good performance of filtering policies in terms of both the overall operating costs, and the demand that is served.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batta, R. (1988). “Single-Server Queueing-Location Models with Rejection.” Transportation Sci. 22, 209–216.
Bazaraa, M.S., H.D. Sherali, and C.M. Shetty. (1993). Nonlinear Programming: Theory and Algorithms. New York: John Wiley Interscience.
Carrizosa, E., E. Conde, and M. Mñoz. (1998). “Admission Policies in Loss Queueing Models with Heterogeneous Arrivals.” Management Sci. 44(3), 311–320.
Chiu, S.S. and R.C. Larson. (1985). “Locating an n-Server Facility in a Stochastic Environment.” Comp. Oper. Res. 12, 509–516.
Frenk, J.B.G., M. Labbé, and S. Zhang. (1993). “A Note on a Stochastic Location Problem.” Oper. Res. Letters 13, 213–214.
Hakimi, S.L. (1964). “Optimum Distribution Centers and Medians of a Graph.” Oper. Res. 12, 450–459.
Hansen, P., M.V. Poggi de Aragao, and C.C. Ribeiro. (1991). “Hyperbolic 0-1 Programming and Query Aptimization in Information Retrieval.” Math. Programming 52, 255–263.
Johnson, S.M. (1954). “Optimal Two- and Three-Stage Production Schedules with Set-Up Times Included.” Naval Res. Logistic Quarterly 1, 61–68.
Lippman, S.A. and S.H. Ross. (1971). “The Streetwalker's Dilemma: A Job Shop Model.” SIAM J. Applied Mathematics 20, 336–342.
Medhi, J. (1991). Stochastic Models in Queueing Theory. Academic Press.
Mehlhorn, K. and S. Näher. (1999). LEDA Library, Version 4.0. Sasbrücken: Max-Planck-Institut für Informatik.
Schaible, S. (1995). “Fractional Programming.” In Horst R. and Pardalos (eds.), Handbook of Global Optimization. Kluver Academic, pp. 495–608.
Xu, S.H., R. Righter, and G. Shantikumar. (1992). “Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel.” Oper. Res. 40, 1126–1138.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fernández, E., Hinojosa, Y. & Puerto, J. Filtering Policies in Loss Queuing Network Location Problems. Ann Oper Res 136, 259–283 (2005). https://doi.org/10.1007/s10479-005-2048-y
Issue Date:
DOI: https://doi.org/10.1007/s10479-005-2048-y