Analysis of Feedback Retrial Queue with Starting Failure and Server 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.

Steady state analysis of batch arrival feedback retrial queue with two phases of service, negative customers, Bernoulli vacation and server breakdown

International Journal of Mathematics in Operational Research ◽

10.1504/ijmor.2015.071276 ◽

2015 ◽

Vol 7 (5) ◽

pp. 519 ◽

Cited By ~ 6

Author(s):

P. Rajadurai ◽

V.M. Chandrasekaran ◽

M.C. Saravanarajan

Keyword(s):

Steady State ◽

Retrial Queue ◽

Batch Arrival ◽

Negative Customers ◽

Steady State Analysis ◽

Server Breakdown ◽

Two Phases ◽

Bernoulli Vacation ◽

Steady-State Analysis of Unreliable Preemptive Priority Retrial Queue with Feedback and Two-Phase Service Under Bernoulli Vacation

Trends in Mathematics - Advances in Algebra and Analysis ◽

10.1007/978-3-030-01120-8_47 ◽

2018 ◽

pp. 425-435

Author(s):

S. Yuvarani ◽

M. C. Saravanarajan

Keyword(s):

Steady State ◽

Retrial Queue ◽

Preemptive Priority ◽

Two Phase ◽

Steady State Analysis ◽

Bernoulli Vacation ◽

Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

Applied Mathematical Modelling ◽

10.1016/j.apm.2006.03.032 ◽

2007 ◽

Vol 31 (6) ◽

pp. 1079-1091 ◽

Cited By ~ 22

Author(s):

Gautam Choudhury ◽

Lotfi Tadj ◽

Madhuchanda Paul

Keyword(s):

Steady State ◽

Two Phase ◽

Steady State Analysis ◽

Multiple Vacation ◽

Bernoulli Vacation ◽

Modelling customers’ impatience with discouraged arrival and retention of reneging

Operations Research and Decisions ◽

10.37190/ord210304 ◽

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

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595906000929 ◽

2006 ◽

Vol 23 (02) ◽

pp. 247-271 ◽

Cited By ~ 27

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.

Steady state analysis of an M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule

Applied Mathematical Modelling ◽

10.1016/j.apm.2007.09.020 ◽

2008 ◽

Vol 32 (12) ◽

pp. 2480-2489 ◽

Cited By ~ 21

Author(s):

Gautam Choudhury

Keyword(s):

Steady State ◽

Two Phase ◽

Steady State Analysis ◽

Bernoulli Vacation ◽

Analysis of an M/G/1 retrial queue with Bernoulli vacation, two types of service and starting failure

International Journal of Artificial Intelligence and Soft Computing ◽

10.1504/ijaisc.2017.088889 ◽

2017 ◽

Vol 6 (3) ◽

pp. 222 ◽

Cited By ~ 2

Author(s):

D. Arivudainambi ◽

M. Gowsalya

Keyword(s):

Retrial Queue ◽

Starting Failure ◽

Analysis of an M/G/1 retrial queue with Bernoulli vacation, two types of service and starting failure

International Journal of Artificial Intelligence and Soft Computing ◽

10.1504/ijaisc.2017.10009794 ◽

2017 ◽

Vol 6 (3) ◽

pp. 222

Author(s):

M. Gowsalya ◽

D. Arivudainambi

Keyword(s):

Retrial Queue ◽

Starting Failure ◽

Communications in Computer and Information Science - Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation ◽

Cost Analysis of an Unreliable Retrial Queue Subject to Balking, Bernoulli Vacation, Two Types of Service and Starting Failure

10.1007/978-981-13-0716-4_16 ◽

2018 ◽

pp. 193-204

Author(s):

D. Arivudainambi ◽

M. Gowsalya

Keyword(s):

Cost Analysis ◽

Retrial Queue ◽

Starting Failure ◽

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

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

10.35940/ijitee.i8985.078919 ◽

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.