Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
Queueing Systems: Theory and Applications
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Queueing Systems: Theory and Applications
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Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
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Manufacturing & Service Operations Management
A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging
Queueing Systems: Theory and Applications
Fluid Limit of the M/M/1+GI-EDF Queue
SAINT-W '05 Proceedings of the 2005 Symposium on Applications and the Internet Workshops
The impact of reneging in processor sharing queues
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Mathematics of Operations Research
Customer Abandonment in Many-Server Queues
Mathematics of Operations Research
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
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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.