Delay Analysis of Orderly Reattempts in Retrial Queueing System with Phase Type Retrial Time

2013 ◽  
Vol 17 (5) ◽  
pp. 822-825 ◽  
Author(s):  
M. S. Kumar ◽  
K. Sohraby ◽  
Kiseon Kim
Keyword(s):  
Queueing System ◽  
Delay Analysis ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Phase Type

scholarly journals An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 758
Author(s):  
P. Rajadurai ◽  
R. Santhoshi ◽  
G. Pavithra ◽  
S. Usharani ◽  
S. B. Shylaja
Keyword(s):  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
Multi Phase ◽  
Number Of Customers

A multi phase retrial queue with optional re-service and multiple working vacations is considered. The Probability Generating Function (PGF) of number of customers in the system is obtained by supplementary variable technique. Various system performance measures are discussed. 

scholarly journals Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

2016 ◽  
Vol 53 (4) ◽  
pp. 1098-1110 ◽  
Author(s):  
Tuǧrul Dayar ◽  
M. Can Orhan
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generator Matrix ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Phase Type ◽  
Necessary And Sufficient ◽  
Infinite State

Abstract A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed.

scholarly journals STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT
Keyword(s):  
Queueing System ◽  
Stability Domain ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Single Orbit ◽  
Transmission Control Protocols ◽  
Regenerative Approach ◽  
The Stability ◽  
Multi Access

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.

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