Optimal Server Allocation in a System of Multi-Server Stations

Management Science · 1987 · Volume 33 · Issue 9

Abstract

Consider a closed queueing network (Gordon and Newell [Gordon, W. J., G. F. Newell. 1967. Closed queueing networks with exponential servers. Oper. Res. 15 252–267.]) with a set of stations. The service rate at each station is an increasing concave function of the number of jobs at that station. Suppose there also exists a station that has c (≥1) parallel servers, each of which has a fixed service rate. We show that the throughput of this network is an increasing concave function with respect to c . This result is then applied to solve the optimal server allocation problem in a system of multi-server stations with a fixed buffer capacity (for the total number of jobs) at each station. For a single-station system, the simultaneous optimal allocation of both servers and buffer capacity is also studied.

Keywords

closed queueing network, concavity of throughput, optimal server/buffer allocation

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