On the theory of queues with many servers

Queues with infinitely many servers

— In the time interval (0, oo) calls arrive in a téléphone exchange in accordance with a récurrent process. There are an unlimited number ofavailable Unes. The holding times are mutually independent and identically distributed positive rondom variables and are independent of the arrivai times. In this paper we détermine the limit distribution of the number of the busy Unes at the arrivai of the...

Queues with Many Servers and Impatient Customers

The asymptotic many-server queue with abandonments, G/GI/N +GI , is considered in the qualityand efficiency-driven (QED) regime. Here the number of servers and the offered load are related via the square-root rule, as the number of servers increases indefinitely. QED performance entails short waiting times and scarce abandonments (high quality) jointly with high servers’ utilization (high effic...

Fluid Limits of Many-servers Queues with Reneging

This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if the time before possible entry into service exceeds the patience time. The dynamics of the system is represented in terms of a pair of measure-valued process...

Heavy Traffic Limits for Queues with Many Deterministic Servers

Consider a sequence of stationary GI/D/N queues indexed by N ↑ ∞, with servers’ utilization 1 − β/√N , β > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift −β. This further implies a corresponding limit for the number of customers in the system, an easily computable non-degenerate limiting delay probability in te...

On the Theory of Queues with Many Servers0