New perspectives on the Erlang-A queue. (March 2019)

• Record Type: Journal Article
• Authors: Daw, Andrew; Pender, Jamol
• Is Part Of: Advances in applied probability. Volume 51:Number 1(2019)
• Page Start: 268
• Page End: 299
• Publication Date: 2019-03
• Subjects: Multiserver queue, -- abandonment, -- dynamical system, -- asymptotics, -- time-varying rate, -- moments, fluid limit, -- Erlang-A queue, -- functional forward equation, -- moment generating function; Primary 60K25, -- Secondary 90B22, -- 62L20; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2019.11
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: The nonstationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large-scale multiserver service systems that may experience customer abandonments, such as call centers, hospitals, and urban mobility systems. In this paper we develop novel approximations to all of its transient and steady state moments, the moment generating function, and the cumulant generating function. We also provide precise bounds for the difference of our approximations and the true model. More importantly, we show that our approximations have explicit stochastic representations as shifted Poisson random variables . Moreover, we are also able to show that our approximations and bounds also hold for nonstationary Erlang-B and Erlang-C queueing models under certain stability conditions.