M/G/1 Subject to an Initial Quorum of Customers.
GEORGE MASON UNIV FAIRFAX VA DEPT OF OPERATIONS RESEARCH AND APPLIED STATISTICS
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The model MG1 is modified in the following manner. The server is idled when he runs out of customers and resumes serving when the m1st customers arrives, where m or 0 m1 is referred to as the initial quorum and m is the maximal queue size and system size while the server idles or vacations. The modified model is designated as MGAm. When m0 we have the regular MG1. In Section 1 we derive the omni-equations for the backlog process B equation 1.17 and for the delay process w equation 1.24 by exploiting the simple relation between B and w in MG1m, a relation which results in equation 1.12. In Section 2 we derive several composition properties for the backlog and for the delay. In particular, equation 2.8 says that the backlog is distributed like the sum of the backlog in MG1 and of a random variable which depends on the service time and equation 2.9 says that the delay is distributed like the sum of the delay in MG1 and of a random variable which depends on the service time and on the interarrival time. Keywords Computer networks Local area networks Queueing models. Author
- Operations Research