scholarly journals Multiserver Queue with Guard Channel for Priority and Retrial Customers

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Kazuki Kajiwara ◽  
Tuan Phung-Duc

This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.

2021 ◽  
Vol 13 (04) ◽  
pp. 85-100
Author(s):  
Dang Thanh Chuong ◽  
Hoa Ly Cuong ◽  
Pham Trung Duc ◽  
Duong Duc Hung

In this article, a retrial queueing model will be considered with persevering customers for wireless cellular networks which can be frequently applied in the Fractional Guard Channel (FGC) policies, including Limited FGC (LFGC), Uniform FGC (UFGC), Limited Average FGC (LAFGC) and Quasi Uniform FGC (QUFGC). In this model, the examination on the retrial phenomena permits the analyses of important effectiveness measures pertained to the standard of services undergone by users with the probability that a fresh call first arrives the system and find all busy channels at the time, the probability that a fresh call arrives the system from the orbit and find all busy channels at the time and the probability that a handover call arrives the system and find all busy channels at the time. Comparison between four types of the FGC policy can befound to evaluate the performance of the system.


2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.


Author(s):  
Kalyanaraman Rathinasabapathy

A retrial queueing system with two types of batch arrivals is considered. The arrivals are called type I and type II customers. The type I customers arrive in batches of size k with probability c_k and type II customers arrive in batches of size k with probability d_k. Service time distributions are identical independent distributions and are different for both type of customers. If the arriving customers are blocked due to server being busy, type I customers are queued in a priority queue of infinity capacity whereas type II customers entered into retrial group in order to seek service again after a random amount of time. For this model the joint distribution of the number of customers in the priority queue and in the retrial group in closed form is obtained. Some particular models and operating characteristics are obtained. A numerical study is also carried out.


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