State Dependence in M/G/1 Server-Vacation Models

Abstract

This paper examines a generalization of the exhaustive and one-at-a-time-discipline M/G/1 server vacation models. This alternative model is viewed as a state-dependent (nonvacation) M/G/1 queue in which the original service times are extended to include a (possibly zero length) state-dependent vacation after each service. Such a vacation policy permits greater flexibility in modeling real problems, and does, in fact, subsume most prior M/G/1 approaches. This device reveals a fundamental decomposition somewhat like that previously established for the classical vacation disciplines. In addition, necessary and sufficient conditions for system ergodicity are established for the state-dependent vacation policy, and some comments are offered on computations.

Subgeometric rates of convergence for a class of continuous-time Markov process

“…The other queues can be studied more easily via the same method. For more details about M/G/1(E, MV), see [5], [7], and [10]. This queue is obtained by introducing the strategy of exhaustive service and multiple vacation to the classical M/G/1 queue: once the system has no customers, the server begins a vacation of random length V immediately.…”

The BMAP/G/1 vacation queue with queue-length dependent vacation schedule

“…Let P(n,t) be the matrix whose (/, j) entry is Pjj(n, t), the conditional probability that n arrivals occur in (0, t ] and the arrival phase is j at time t, given that the phase at oo time 0 is /. The matrix generating function P*(z,t) = ^2 P(n,t)z n (\z\ < 1) of the [3] The BMAP/G/l vacation queue with queue-length dependent vacation schedule 209 sequence of matrices {P(n, t)} is then given by…”

On functionals of a marked Poisson process observed by a renewal process

“…The renewal process observing the Poisson process can represent multiple vacations rendered by a server [2,3,12,13,14,15,16,17,19]. In other words, when the server leaves the system, it generates a sequence of vacation (or maintenance) segments each of which ends up with the server returning to the system and checking on its status.…”