Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 1, pp. 39--51

TRANSIENT ANALYSIS OF THRESHOLD $T$-POLICY $M/M/1$ QUEUES WITH SERVER CONTROL

By

KANWAR SEN and RITU GUPTA, University of Delhi

SUMMARY. The transient distribution for the number in the system is derived through Lattice Path method for the following generalization of $M/M/l T$-policy queues, considered to prevent frequent vacations. In this system the server remains busy as long as there are at least L customers waiting. Further if the server after completing M services finds the queue length L he proceeds on a vacation of length T. And the server is allowed to take multiple vacation each of duration T and starts serving only when the number of customers in the queue becomes N. Further more meaningful probabilistic interpretations are provided to the transient probabilities computed here in. Also the results of $M/M/l$ threshold $T$-policy with restricted vacations and $(M, N)$-policy are checked.

AMS (1989) subject classification. Primary 60K25; secondary 60J15.

Key words and phrases. Busy period, discretized $M/M/l(T,M,N,L) model, idle period, lattice path, $M/M/l(T,M,N,L) model, (M,N) policy, non-exhaustive service, segment, threshold conditions, $T$-policy, transient probabilities.

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