2008/02/18 by Pascal Moyal, Moyal, Pascal
Business, Management and Accounting · Mathematics · #60B12 (Secondary) #60F17 (Primary) #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60B12 #msc:60F17 #msc:60K25
paper · pdf · doi:10.48550/arxiv.0802.2495
arxiv created 2008/02/18 · openalex publication_date 2008/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times). In the particular case of a single server operating in First in, First out, we prove the existence (in some cases, on an enlarged probability space) of a stationary workload. This is done by studying stochastic recursions under the Palm settings, and by stochastic comparison of stochastic recursions.