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Title: Diffusion approximations for open Jackson networks with reneging
Authors: Huang, J.
Zhang, H. 
Keywords: Abandonment-count process
Diffusion approximation
Open Jackson network
Queue length process
Issue Date: Aug-2013
Citation: Huang, J., Zhang, H. (2013-08). Diffusion approximations for open Jackson networks with reneging. Queueing Systems 74 (4) : 445-476. ScholarBank@NUS Repository.
Abstract: We consider generalized Jackson networks with reneging in which the customer patience times follow a general distribution that unifies the patience time without scaling adopted by Ward and Glynn (Queueing Syst 50:371-400, 2005) and the patience time with hazard rate scaling and unbounded support adopted by Reed and Ward (Math Oper Res 33:606-644, 2008). The diffusion approximations for both the queue length process and the abandonment-count process are established under the conventional heavy traffic limit regime. In light of the recent work by Dai and He (Math Oper Res 35:347-362, 2010), the diffusion approximations are obtained by the following four steps: first, establishing the stochastic boundedness for the queue length process and the virtual waiting time process; second, obtaining the C-tightness and fluid limits for the queue length process and the abandonment-count process; then third, building an asymptotic relationship between the abandonment-count process and the queue length process in terms of the customer patience time. Finally, the fourth step is to get the diffusion approximations by invoking the continuous mapping theorem. © 2013 Springer Science+Business Media New York.
Source Title: Queueing Systems
ISSN: 02570130
DOI: 10.1007/s11134-012-9335-5
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