Queue Size Distribution on a New ND Policy Geo/G/1 Queue and Its Computation Designs

Rongxiu Wang

doi:10.1155/2021/6364352

Abstract

This paper examines a new ND policy in the discrete-time Geo/G/1 queue. Under this ND policy, the idle server restarts its service when the N and D policies are simultaneously satisfied. By two classifications of the customers, the probability-generating function and the probabilistic analysis, the steady-state queue size distributions at a departure time and an arbitrary time t + are studied. Finally, the theoretical results are applied to the power-saving problem of a wireless sensor network. To improve model universality and numerical slowness, some computation designs are carried out. Under the N, D, and two ND policies, the numerical experiments are presented to obtain the optimal policy thresholds and the corresponding minimum power consumptions are compared.

Highlights

We introduce a new ND policy in the discretetime Geo/G/1 queue, obtain the steady-state queue size distribution, and conduct some computation designs in the minimum power consumption of a wireless sensor network
Under the new ND policy, when the number of the customers in the queueing system reaches at least N and, at the same time, the sum of the service time periods of all waiting customers is greater than a given nonnegative integer D, the idle server begins to offer its service for the waiting customers
The ND policy 2 may be ineffective when the setup power consumption is much larger than the holding power consumption of the data packet in a busy cycle

Summary

Introduction

We introduce a new ND policy in the discretetime Geo/G/1 queue, obtain the steady-state queue size distribution, and conduct some computation designs in the minimum power consumption of a wireless sensor network. As far as known to the author, for the existing papers on the discrete-time queues with the N policy and genuine D policy, the queue size distribution obtained in this work is new It is useful and important when a power consumption function is constructed to analyze the optimal ND policy at a minimum power value. Gu et al [1] and Lan and Tang [2] applied a probability decomposition method to obtain the queue size distributions in the discrete-time Geo/G/1 queues with the ND policy 2 They avoided the dependence of the service time periods of the customers who arrive during the idle period, and the D policy they considered was not a genuine D policy, which was pointed out by Liu et al [3, 9]. ΦN,D: the service time backlog of all waiting customers at the start of a busy period

Preliminaries

Computation Designs in the Optimal Power Control of a WSN