Abstract
A finite-capacity queueing model with the arrival stream of messages governed by the compound Poisson process and generally-distributed processing times is investigated. Whenever the system becomes empty (the server becomes idle), a number of deterministic independent vacations of equal length are initialized as far as at least one message is detected in the accumulating buffer at the completion epoch of one of them. During vacations the service process is suspended completely, while after finishing the last vacation it restarts normally. Identifying Markov moments in the evolution of the system and using the Korolyuk’s potential method, the compact-form representation for the transient queue-size distribution conditioned by the initial buffer state is found in terms of its Laplace transform. The considered model has potential applications in modeling the energy saving LTE DRX mechanism. A detailed simulation and numerical study is attached.
Highlights
G LOBAL challenges related to the need to save energy are a permanent motivation to look for new solutions and techniques that could be used in more effective energy management and monitoring the phenomenon of its consumption
Energy saving is of particular importance in the operation of wireless networks (Wi-Fi, LTE, wireless sensor networks etc.) where nodes/mobile stations are usually powered by batteries
Applying analytical approach based on the idea of embedded Markov chain, continuous version of the formula of total probability and Korolyuk’s potential method, a compact-form representation for the Laplace transform of the queue-size distribution conditioned by the initial buffer state is obtained
Summary
G LOBAL challenges related to the need to save energy are a permanent motivation to look for new solutions and techniques that could be used in more effective energy management and monitoring the phenomenon of its consumption. A finite-buffer model with Poisson arrival stream and generally-distributed service times is studied in [16] under multiple vacation policy. In [15] new results for a general-type GI/G/1 model with batch arrivals of messages and exponentially-distributed server vacations are derived It is obtained the Laplace transform of the joint distribution of the first busy period, the first vacation period and the number of messages served during the first busy period. We study a finite-buffer queueing model with batch Poisson input flow, generally distributed service times operating under multiple vacation policy with deterministic (constant) durations of successive vacations. Applying analytical approach based on the idea of embedded Markov chain, continuous version of the formula of total probability and Korolyuk’s potential method, a compact-form representation for the Laplace transform of the queue-size distribution conditioned by the initial buffer state is obtained.
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