Analysis Of G_t/H₂^*/S_t+M Queueing Model

In the service system,the arrival rate of customers is time-varying,and there are interruptions in the service process.The service system will adjust the number of servers according to specific conditions to ensure the effective use of resources and create greater benefits.This paper studied theG_t/H ₂^*/s_t+M queue model,which mainly analyzes the heavy-traffic limit about the head-of-line waiting time and the number in queue.First of all,introduce theG_t/H ₂^*/s_t+M queue model,given model assumptions,divide the system into busy and idle periods,analyze the head-of-line waiting time at the busy interval,analyze the head-of-line waiting time through the numbers of customers entering the service,and establish the functional weak law of large numbers(FWLLN)and functional central limit theorem(FCLT)of head-of-line waiting time.The conclusion is proved in two steps,first,the tightness of{W_n}is showed by stochastic bounded and continuous modulus infinitesimal,second,the convergence limit of subsequence is explained.Secondly,analyze the number in queue inG_t/H ₂^*/?queue model by two-parameter stochastic process,the number in queue is represented by sequence experience process,establish the FWLLN and FCLT of the number in queue,respectively,under the scale of FWLLN and FCLT,the stochastic process is decomposed,use the weak convergence method to prove the conclusion.Finally,simulate theG_t/H ₂^*/s+M queue model.Algorithm analysis is carried out first,and given the arrival rate function and the abandonment rate,the number of customers in queue and abandoners are simulated,obtain the different of the abandonment rate in the system when the number of servers is the same and the p is different.