Please use this identifier to cite or link to this item:
|Title:||Diffusion approximations for open Jackson networks with reneging|
Open Jackson network
Queue length process
|Source:||Huang, J., Zhang, H. (2013-08). Diffusion approximations for open Jackson networks with reneging. Queueing Systems 74 (4) : 445-476. ScholarBank@NUS Repository. https://doi.org/10.1007/s11134-012-9335-5|
|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|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Jan 15, 2018
WEB OF SCIENCETM
checked on Nov 17, 2017
checked on Jan 20, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.