基于Min(N,D,V)-策略和单重休假的M/G/1排队系统队长分布的瞬态和稳态解

Transient and Equilibrium Solutions of Queue Length Distribution for M/G/1 Queueing System with Min(N,D,V)-policy and Single Server Vacation

本文主要研究服务员单重休假且在休假时间中根据Min(N,D,V)–控制策略可立即中断休假的M=G=1排队系统.运用全概率分解技术和拉普拉斯变换工具,讨论在任意初始状态条件下队长的瞬态和稳态性质,得到了队长分布瞬态解的拉普拉斯变换表达式.在此基础上,直接获得了便于作数值计算的队长分布稳态解的递推表达式.进一步,给出了稳态队长的随机分解结构、附加队长分布的显示表达式,以及在一些特殊情形下的相应结果.最后,通过数值实例考察了附加队长分布对系统参数的敏感性,分析参数不同取值对系统运行性能的影响.

This paper considers the M=G=1 queueing system with single server vacation which can be interrupted immediately according to the Min(N,D,V)-policy.By applying the total probability decomposition technique and the Laplace transformation,the transient and steadystate properties of the queue length from any initial state are discussed,and the Laplace transformation expression of the transient solution of queue length distribution is obtained.Moreover,we derive the recursive expressions of the equilibrium solution of queue length distribution for convenient calculation.Furthermore,we propose the stochastic decomposition structures of the steady-state queue length,the explicit expressions for the probability distribution of the additional queue length and the corresponding results for some special cases.Finally,by numerical examples,we discuss the sensitivity of the steady state queue length distribution towards system parameters and analyze the influence of different parameters on system performance.