The physics of the Mt/G/ ∞ symbol Queue
Operations Research
A heavy-traffic analysis of a closed queueing system with a GI/\infty service center
Queueing Systems: Theory and Applications
Control and recovery from rare congestion events in a large multi-server system
Queueing Systems: Theory and Applications
Strong approximations for Markovian service networks
Queueing Systems: Theory and Applications
Fluid Models for Multiserver Queues with Abandonments
Operations Research
The last departure time from an Mt/G/∞ queue with a terminating arrival process
Queueing Systems: Theory and Applications
Large-time asymptotics for the Gt/Mt/st+GIt many-server fluid queue with abandonment
Queueing Systems: Theory and Applications
Exact asymptotic for infinite-server queues
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment
Operations Research
The Impact of Dependent Service Times on Large-Scale Service Systems
Manufacturing & Service Operations Management
Two-parameter heavy-traffic limits for infinite-server queues with dependent service times
Queueing Systems: Theory and Applications
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In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic limits for two-parameter stochastic processes. We consider the random variables Q e (t,y) and Q r (t,y) representing the number of customers in the system at time t that have elapsed service times less than or equal to time y, or residual service times strictly greater than y. We also consider W r (t,y) representing the total amount of work in service time remaining to be done at time t+y for customers in the system at time t. The two-parameter stochastic-process limits in the space D([0,驴),D) of D-valued functions in D draw on, and extend, previous heavy-traffic limits by Glynn and Whitt (Adv. Appl. Probab. 23, 188---209, 1991), where the case of discrete service-time distributions was treated, and Krichagina and Puhalskii (Queueing Syst. 25, 235---280, 1997), where it was shown that the variability of service times is captured by the Kiefer process with second argument set equal to the service-time c.d.f.