Logarithmic asymptotics for a single-server processing distinguishable sources
Duffy, Ken R. and Malone, David (2008) Logarithmic asymptotics for a single-server processing distinguishable sources. Mathematical Methods of Operations Research , 68 (3). pp. 509-537. ISSN 1432-5217
We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution.We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results.
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