基于Max(N,D)策略的MG1排队系统的稳态指标

Steady-state indices of MG1 queueing system based on the Max(N,D)-policy

考虑一个由N策略和D策略同时控制的MG1排队系统.当顾客的到达个数至少为N个同时等待顾客的服务时间之和大于某非负实数D时,空闲的服务台重新开始服务顾客(称此服务启动策略为Max(N,D)策略).在此策略下,由于闲期到达顾客的服务时间是条件相依的,故队长的随机分解不再成立.通过将顾客分成两类,并借助拉普拉斯变换和概率分析,研究了该排队系统的稳态队长分布、稳态闲期和忙期分布、稳态服务时间积压量分布以及顾客的稳态逗留时间分布.数值算例分析了N、D和Max(N,D)策略对稳态平均队长的影响.在数值上获得了系统稳态费用最小的最优策略临界值,并比较了N、D、Max(N,D)和Min(N,D)策略的优越性.

This paper considers an MG1 queueing system controlled by the N and D policies.When the number of arriving customers is larger or equal to N,and the sum of service times of waiting customers exceeds a predetermined non-negative real number D,the idle server resumes its service(this service start policy is called the Max(N,D) policy).Under this policy,since the service times of customers arriving during the idle period are conditionally dependent,the stochastic decomposition of queue length does not hold.By two classifications of customers,Laplace transform and probabilistic analysis,the steadystate distributions of queue length,idle and busy periods,service time backlog,and sojourn time,are studied.The effect of N,D and Max(N,D) policies on mean steady-state queue length is numerically analyzed.Numerically,the optimal threshold policies minimizing the steady-state cost are obtained,and the superiority of N,D,Max(N,D) and Min(N,D) policies is compared.