Asymptotic study on change point problem for waiting time data in a single server queue

摘要

Very often it is impracticable or costly to collect all information regarding the arrival times and service times of queue. In such a situation, it is therefore necessary to develop sampling plans which do not require the full information on interarrival or service times. This paper is concerned with the study of change point problem for waiting time data in GI/G/1 queueing system in which the interarrival times {U-t, t >= 1} and the service times {V-t, t >= 1} of the tth customer are two independent sequences of independent and identically distributed random variables. A test statistics regarding the acceptance of the null hypothesis has been developed and its asymptotic properties have been studied. The results are illustrated with the help of an M/M/1 queue and then established through simulation.