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- Title
Steady-state analysis of shortest expected delay routing.
- Authors
Selen, Jori; Adan, Ivo; Kapodistria, Stella; Leeuwaarden, Johan
- Abstract
We consider a queueing system consisting of two nonidentical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with nonidentical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product forms that can be determined recursively. The resulting series expression is directly amenable to numerical calculations and it also provides insight into the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.
- Subjects
QUEUEING networks; CLIENT/SERVER computing equipment; MARKOV processes; POISSON processes; RANDOM walks; ROUTING (Computer network management)
- Publication
Queueing Systems, 2016, Vol 84, Issue 3/4, p309
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-016-9497-7