Analysis of Feedback Retrial Queue with Starting Failure and Server Vacation

2016 ◽  
pp. 71-96
Author(s):  
K. Sathiya Thiyagarajan ◽  
G. Ayyappan
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Retrial Queue ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Steady State Analysis ◽  
Starting Failure ◽  
Dependent Probability ◽  
Bernoulli Vacation

In this chapter we discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability or may wait for serving the next customer. Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.

scholarly journals Modelling customers’ impatience with discouraged arrival and retention of reneging

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pallabi Medhi
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Stochastic Modelling ◽  
Steady State Solution ◽  
Single Server ◽  
Finite Buffer ◽  
System Parameters ◽  
Retention Of Reneged Customers

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention of reneged customers. Markov process is used to derive the steady-state solution of the model. Closed form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

2006 ◽  
Vol 23 (02) ◽  
pp. 247-271 ◽  
Author(s):  
IVAN ATENCIA ◽  
PILAR MORENO
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing System ◽  
Retrial Queue ◽  
System Size ◽  
Stochastic Decomposition ◽  
Recursive Procedure ◽  
Server Breakdown

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

scholarly journals M/M/1 Queueing system with Customer Balking and Reneging

2019 ◽  
Vol 8 (9) ◽  
pp. 2636-2646
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
Probability Generating Functions ◽  
Multiple Vacation ◽  
Steady State Probabilities ◽  
Explicit Expressions

This paper deals with an M/M/1 queueing system with customer balking and reneging. Balking and reneging of the customers are assumed to occur due to non-availability of the server during vacation and breakdown periods. Steady state probabilities for both the single and multiple vacation scenarios are obtained by employing probability generating functions. We evaluate the explicit expressions for various performance measures of the queueing system.

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