Paper Info
Title
A Unified Approach to Diffusion Analysis of Queues with General Patience-Time Distributions
Abstract
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the diffusion-scaled abandonment process is asymptotically close to a function of the diffusion-scaled queue length process under appropriate conditions. The second step is to construct a continuous mapping not only to characterize the system dynamics using the system primitives, but also to help verify the conditions needed in the first step. The diffusion approximations can then be obtained by applying the continuous mapping theorem. The approach has two advantages: (i) it provides a unified procedure to establish the diffusion approximations regardless of the structure of the queueing model or the type of patience-time scaling; and (ii) it makes the diffusion analysis of queues with customer abandonment essentially the same as the diffusion analysis of queues without customer abandonment. We demonstrate the application of this approach via the single-server system with Markov-modulated service speeds in the traditional heavy-traffic regime and the many-server system in the Halfin-Whitt regime and the nondegenerate slowdown regime.
Year
DOI
Venue
2016
10.1287/moor.2015.0772
MATHEMATICS OF OPERATIONS RESEARCH
Keywords
Field
DocType
customer abandonment,single-server queue,many-server queue,heavy traffic,Halfin-Whitt regime,nondegenerate slowdown regime,diffusion approximation
Patience,Mathematical optimization,Continuous mapping theorem,Computer science,Queue,Degeneracy (mathematics),Queueing theory,System dynamics,Scaling,Heavy traffic approximation
Journal
Volume
Issue
ISSN
41
3
0364-765X
Citations 
PageRank 
References 
1
0.36
12
Authors
3
Name
Order
Citations
PageRank
Junfei Huang1202.80
Zhang Hanqin222328.29
Jiheng Zhang3717.90