Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations

Abstract

A finite-buffer M/G/1-type queueing system with exhaustive service and server vacations is considered. The single and multiple vacation policies are investigated separately. In the former case a single vacation is being initialized every time when the system becomes empty. After the vacation the server waits on standby for packets to start the service process. In the multiple vacation policy the server begins successive single vacation periods until at least one packet is present in the system. For both vacation policies systems of integral equations for the transient virtual waiting time v(t) distributions, conditioned by the numbers of packets present in the system at the start epoch, are found. The representations for the twofold Laplace transforms of the conditional distributions of v(t) are obtained and written in compact forms, convenient in numerical treatment. From these formulae stationary distributions of v(t) and their means can be computed via usual operations on transforms. Some numerical illustrations of theoretical results are attached as well.

On buffer overflow duration in a finite-capacity queueing system with multiple vacation policy

“…The compact-form representations for the distributions of the time to buffer overflow are derived in [11] and [12], where the GI/M/1/N-type model and the M/G/1/N-type queue with warm up (setup) and closedown times are analyzed, respectively. Moreover, in [13], [14], [15] and [16] the time-dependent queueing systems with different-type traffic control mechanisms (like e.g. single vacation policy) can be found.…”

On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling

“…In [13] an M/M/1 model subjected to multiple differentiated vacations, customer impatience and a waiting server is investigated. A finite-buffer model with Poisson arrival stream and generally-distributed service times is studied in [16] under multiple vacation policy. Compact-form representation for the Laplace transform of the transient queueing delay is obtained there.…”

Analytical Model of a Wireless Sensor Network (WSN) Node Operation with a Modified Threshold-Type Energy Saving Mechanism

“…Transient (time-dependent, non-stationary) results for queueing systems with multiple (repeated) vacation policy, used as a model of energy saving mechanisms, can be found in [18,19,20,21] (compare also [22,23,24]). In particular, in [18,21] the departure process is investigated in cases of infinite and finite buffer capacities, respectively, while in [19] the queueing delay is investigated (also for the single vacation policy). Similarly, transient analysis of power saving models based on the N -policy can be found in [25] (queueing delay) and [26] (departure process).…”