Stability of parallel queueing systems with coupled service rates
- Discrete Event Dynamic Systems 18(4):447-472, 2008, doi:10.1007/s10626-007-0021-4.
- Preprint: CWI Report PNA-E0613, December 2006.
- Corrected version: January 2010, arXiv:1001.1560.
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp characterization of stability for systems, where the service rate of each queue is decreasing in the number of customers in other queues, and has uniform limits as the queue lengths tend to infinity. The results are illustrated with applications where the stability region may be nonconvex.
Keywords: stability, positive recurrence, multiclass birth and death process, Foster-Lyapunov drift criterion, stochastic comparison, coupled processors
AMS subject classification: 60K25, 90B22, 68M20, 60K20