In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to interrupt the vacation and return back to the normal working period, if there are at least N customers waiting in the system at a service completion instant during the working vacation period. Otherwise, the server continues the vacation until the system is nonempty after a vacation ends or there are at least N customers after a service ends. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions for the stationary queue length. Moreover, we demonstrate stochastic decomposition structures of the queue length and waiting time, and obtain the distributions of the additional queue length and additional delay for the case N = 2 . Finally, numerical examples are presented.
Majid, Shakir and Manoharan, P.
Analysis of an M/M/1 Queue With Working Vacation and Vacation Interruption,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
1, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss1/2