Remaining loads in a PH/M/c queue with impatient customers

2022/04/21 by Anders Rygh Swensen, Swensen, Anders Rygh
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2204.09988

openalex publication_date 2022/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There are two contributions to the literature in this note. Firstly, we point out that under some weak conditions the result in Swensen (1986) on the remaining loads in a GI/M/c queue with impatient customers, derived under the assumption that the distribution of inter-arrival times is Coxian, is also valid for the more general phase type distribution. From this result the distributions of the virtual and the actual waiting time can easily be obtained. Secondly, the relation to an alternative expression for the distribution of the virtual waiting time derived by Kawanishi and Takine (2015) is also discussed.

Related

• Stationary Distribution Convergence of the Offered Waiting Processes for GI/GI/1+GI Queues in Heavy Traffic
• Stationary Distribution Convergence of the Offered Waiting Processes in Heavy Traffic under General Patience Time Scaling
• M/M/c Queues and the Poisson Clumping Heuristic
• M/G/1-FIFO Queue with Uniform Service Times
• The asymptotic behavior o queues with time-varying arrival rates