On the exact asymptotics of the busy period in GI/G/1 queues
نویسندگان
چکیده
In this paper we study the busy period in GI/G/1 work-conserving queues. We give the exact asymptotics of the tail distribution of the busy period under the light-tailed assumptions. We also study the workload process in the M/G/1 system conditioned to stay positive.
منابع مشابه
Exponential Approximations for Tail Probabilities in Queues: Sojourn Time and Workload
In this paper, we focus on simple exponential approximations for steady-state tail probabilities in G/GI/1 queues based on large-time asymptotics. We relate the large-time asymptotics for the steady-state waiting time, sojourn time and workload. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical...
متن کاملTransient and Busy Period Analysis of the Gi/gi1 Queue as a Hilbert Factorization Problem
In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace tran...
متن کاملA Suality Relation for Busy Cycles in GI/G/1 Queues
Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle in M/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dual GI/M/1. In this note, we generalize this duality relation to GI/G/1 queues with modif...
متن کاملA MAP/G/1 Queue with Negative Customers
In this paper, we consider a MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in Section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. B...
متن کاملAn MAP/G/1 Queue with Negative Customers
In this paper, we consider an MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in Section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. ...
متن کامل