A queueing system with general-use and limited-use servers
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We consider a queueing system with two types of servers and two types of customers. General-use servers can provide service to either customer type while limited-use servers can be used only for one of the two. Though the apparent Markovian state space of this system is five-dimensional, we show that an aggregation results in an exact two-dimensional representation that is also Markovian. Matrix geometric theory is used to obtain approximations for the mean delay times and other measures of interest for each customer type. We illustrate the methodology by applying it to analyze a token discount policy used by the Triborough Bridge and Tunnel Authority.
Source: Operations Research
Green, Linda. "A queueing system with general-use and limited-use servers." Operations Research 33, no. 1 (1985): 168-182.