An Analysis of the M/G/1 Retrial Queue with Negative Arrivals using a Martingale Technique*

2013 ◽  
Vol 196 (1) ◽  
pp. 11-14
Author(s):  
L. Berdjoudj ◽  
D. Aissani
2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Mohamed Boualem ◽  
Natalia Djellab ◽  
Djamil Aïssani

This paper focuses on stochastic comparison of the Markov chains to derive some qualitative approximations for anM/G/1retrial queue with a Bernoulli feedback. The main objective is to use stochastic ordering techniques to establish various monotonicity results with respect to arrival rates, service time distributions, and retrial parameters.


1998 ◽  
Vol 14 (5) ◽  
pp. 1151-1177 ◽  
Author(s):  
Jeffrey E. Diamond ◽  
Attahiru Sule Alfa
Keyword(s):  

2003 ◽  
Vol 17 (4) ◽  
pp. 487-501 ◽  
Author(s):  
Yang Woo Shin ◽  
Bong Dae Choi

We consider a single-server queue with exponential service time and two types of arrivals: positive and negative. Positive customers are regular ones who form a queue and a negative arrival has the effect of removing a positive customer in the system. In many applications, it might be more appropriate to assume the dependence between positive arrival and negative arrival. In order to reflect the dependence, we assume that the positive arrivals and negative arrivals are governed by a finite-state Markov chain with two absorbing states, say 0 and 0′. The epoch of absorption to the states 0 and 0′ corresponds to an arrival of positive and negative customers, respectively. The Markov chain is then instantly restarted in a transient state, where the selection of the new state is allowed to depend on the state from which absorption occurred.The Laplace–Stieltjes transforms (LSTs) of the sojourn time distribution of a customer, jointly with the probability that the customer completes his service without being removed, are derived under the combinations of service disciplines FCFS and LCFS and the removal strategies RCE and RCH. The service distribution of phase type is also considered.


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