D/M/1 Queue: Policies and Control

2022/10/16 by Steven R. Finch, Finch, Steven
Business, Management and Accounting · #33B99 #34Kxx #44A10 #60K25 (Primary) 60-03 #68Q87 #90-03 (Secondary) #90B22 #Advanced Queuing Theory Analysis #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #History and Overview (math.HO) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2210.08545

openalex publication_date 2022/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equilibrium G/M/1-FIFO waiting times are exponentially distributed, as first proved by Smith (1953). For other client-sorting policies, such generality is not feasible. Assume that interarrival times are constant. Symbolics for the D/M/1-LIFO density are completely known; numerics for D/M/1-SIRO arise via an unpublished recursion due to Burke (1967). Consider a weighted sum of two costs, one from keeping clients waiting for treatment and the other from having the server idle. With this in mind, what is the optimal interarrival time and how does this depend on the choice of policy?

Related

• M/D/1 Queues with LIFO and SIRO Policies
• M/G/1-FIFO Queue with Uniform Service Times
• Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic
• A Bound on the Variance of the Waiting Time in a Queueing System
• When to arrive at a queue with earliness, tardiness and waiting costs