On the Single Server Batch Arrival Retrial Queue with General Vacation Time under Bernoulli Schedule and Two phases of Heterogeneous Service

2008 ◽  
Vol 5 (2) ◽  
pp. 145-160 ◽  
Author(s):  
M. Senthil Kumar ◽  
R. Arumuganathan
Keyword(s):  
Retrial Queue ◽  
Batch Arrival ◽  
Single Server ◽  
Vacation Time ◽  
Two Phases ◽  
Heterogeneous Service ◽  
Bernoulli Schedule

Performance Analysis of an M/G/1 Feedback Retrial Queue with Two Types of Service and Bernoulli Vacation

2016 ◽  
pp. 38-54
Author(s):  
Arivudainambi D ◽  
Gowsalya Mahalingam
Keyword(s):  
Retrial Queue ◽  
Single Server ◽  
Supplementary Variable ◽  
Number Of Customers ◽  
Bernoulli Schedule ◽  
Schedule Mechanism ◽  
Fcfs Discipline ◽  
Bernoulli Vacation

This chapter is concerned with the analysis of a single server retrial queue with two types of service, Bernoulli vacation and feedback. The server provides two types of service i.e., type 1 service with probability??1 and type 2 service with probability ??2. We assume that the arriving customer who finds the server busy upon arrival leaves the service area and are queued in the orbit in accordance with an FCFS discipline and repeats its request for service after some random time. After completion of type 1 or type 2 service the unsatisfied customer can feedback and joins the tail of the retrial queue with probability f or else may depart from the system with probability 1–f. Further the server takes vacation under Bernoulli schedule mechanism, i.e., after each service completion the server takes a vacation with probability q or with probability p waits to serve the next customer. For this queueing model, the steady state distributions of the server state and the number of customers in the orbit are obtained using supplementary variable technique. Finally the average number of customers in the system and average number of customers in the orbit are also obtained.

Expected waiting times in a multiclass batch arrival retrial queue

1986 ◽  
Vol 23 (01) ◽  
pp. 144-154 ◽  
Author(s):  
V. G. Kulkarni
Keyword(s):  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival ◽  
Single Server ◽  
Waiting Room ◽  
Compound Poisson ◽  
Special Cases

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.

Expected waiting times in a multiclass batch arrival retrial queue

1986 ◽  
Vol 23 (1) ◽  
pp. 144-154 ◽  
Author(s):  
V. G. Kulkarni
Keyword(s):  
Waiting Times ◽  
Retrial Queue ◽  
Batch Arrival ◽  
Single Server ◽  
Waiting Room ◽  
Compound Poisson ◽  
Special Cases

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.

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