×

zbMATH — the first resource for mathematics

A simple proof of the optimality of a threshold policy in a two-server queueing system. (English) Zbl 0876.90052
Summary: Lin and Kumar (1984) introduced a control model with a single queue and two heterogeneous servers. They showed, using policy iteration, that the slower server should only be used if the queue length is above a certain level, i.e., the optimal policy is of threshold type. In this note we give a simple iterative proof of this result.

MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Glasserman, P.; Yao, D.D., Monotone optimal control of permutable gsmps, Math. oper. res., 19, 449-476, (1994) · Zbl 0801.60077
[2] Lin, W.; Kumar, P.R., Optimal control of a queueing system with two heterogeneous servers, IEEE trans. automat. control, 29, 696-703, (1984) · Zbl 0546.90035
[3] Viniotis, I.; Ephremides, A., Extension of the optimality of the threshold policy in heterogeneous multiserver queueing systems, IEEE trans. automat. control, 33, 104-109, (1988) · Zbl 0631.90026
[4] Walrand, J., A note on “optimal control of a queueing system with two heterogeneous server”, Systems control lett., 4, 131-134, (1984) · Zbl 0581.60079
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.