2013/05/15 by Fabrice Guillemin, Guillemin, Fabrice, Alain Simonian +1
Business, Management and Accounting · Computer Science · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #Performance (cs.PF) #cs.PF
paper · pdf · doi:10.48550/arxiv.1305.3496
arxiv created 2013/05/15 · openalex publication_date 2013/05/15 · arxiv updated 2013/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As a follow-up to a recent paper considering two symmetric queues, the Shortest Queue First service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming exponentially distributed service times, the bivariate Laplace transform of workloads in each queue is shown to depend on the solution M to a two-dimensional functional equation M = Q1 ⋅ M∘ h1 + Q2 ⋅ M∘ h2 + L with given matrices Q1, Q2 and vector L and where functions h1 and h2 are defined each on some rational curve; solution M can then represented by a series expansion involving the semi-group < h1, h2 > generated by these two functions. The empty queue probabilities along with the tail behaviour of the workload distribution at each queue are characterised.