New Approach for Finding Performance Measures of Continuous-time Server Queue With Negative Customers

Chin, Ching Herny (2018) New Approach for Finding Performance Measures of Continuous-time Server Queue With Negative Customers. Master dissertation/thesis, UTAR.

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Abstract

A single-server continuous-time queue that adopt first come first serve (FCFS) queueing discipline with negative customers is studied. The arrival of a negative customer in the queue will remove one positive customer at the head if the system is not empty (RCH) and only positive customers will receive service. In this research, a fairly general queueing model with negative customers that can represent more wide applications in real world is solved. An alternative approach will be applied to derive a set of equations which is using to find the stationary queue length distributions of this model. In the alternative numerical approach, interarrival time and/or service time distributions of the positive customers are assumed to have Constant Asymptotic Rate (CAR) when time t goes to infinity. Whereas negative customer arrives to the system according to a Poisson process.Expressions will also be derived analytically to find the stationary queue length distribution for the M/M/1, M/CAR/1, GI/M/1 and CAR/CAR/1 queues with negative customers. The stationary probabilities found from the alternative and analytical approaches are used to find the waiting time distribution. Results computed by both the proposed numerical and analytical methods are compared and discussed. All the results will be verified by those obtained from the simulation procedure.

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