Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown

2017 ◽  
Vol 51 (2) ◽  
pp. 485-508 ◽  
Author(s):  
S. Jeyakumar ◽  
B. Senthilnathan
Keyword(s):  
Queueing Model ◽  
Server Breakdown ◽  
Multiple Working Vacations ◽  
Bulk Service ◽  
Working Vacations

scholarly journals GEOM/GEOM[a]/1/ queue with late arrival system with delayed access and delayed multiple working vacations

2014 ◽  
Vol 24 (1) ◽  
pp. 127-143 ◽  
Author(s):  
Jiang Cheng ◽  
Yinghui Tang ◽  
Miaomiao Yu
Keyword(s):  
Queue Length ◽  
Probability Generating Function ◽  
Operator Method ◽  
Analysis Method ◽  
Idle Period ◽  
Arrival Times ◽  
Late Arrival ◽  
Multiple Working Vacations ◽  
Bulk Service ◽  
Working Vacations

This paper considers a discrete-time bulk-service queue with infinite buffer space and delay multiple working vacations. Considering a late arrival system with delayed access (LAS-AD), it is assumed that the inter-arrival times, service times, vacation times are all geometrically distributed. The server does not take a vacation immediately at service complete epoch but keeps idle period. According to a bulk-service rule, at least one customer is needed to start a service with a maximum serving capacity 'a'. Using probability analysis method and displacement operator method, the queue length and the probability generating function of waiting time at pre-arrival epochs are obtained. Furthermore, the outside observer?s observation epoch queue length distributions are given. Finally, computational examples with numerical results in the form of graphs and tables are discussed.

scholarly journals The Discrete-Time Bulk-ServiceGeo/Geo/1Queue with Multiple Working Vacations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jiang Cheng ◽  
Yinghui Tang ◽  
Miaomiao Yu
Keyword(s):  
Discrete Time ◽  
Queue Length ◽  
Busy Period ◽  
Operator Method ◽  
Embedded Markov Chain ◽  
Working Vacation ◽  
Early Arrival ◽  
Multiple Working Vacations ◽  
Bulk Service ◽  
Working Vacations

This paper deals with a discrete-time bulk-serviceGeo/Geo/1queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at timen. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.

Interdependent Queueing Model with Varying Bulk Service

2012 ◽  
Vol 2 (1) ◽  
pp. 109 ◽  
Author(s):  
T. S. R Murthy ◽  
Sivarama Krishna ◽  
G. V. S Raju
Keyword(s):  
Queueing Model ◽  
Bulk Service

scholarly journals Queues with two units connected in series with a multiserver bulk service with accessible and non accessible batch in unit II

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
G. Ayyappan ◽  
S. Velmurugan
Keyword(s):  
Service Time ◽  
Subject Classification ◽  
Geometric Method ◽  
Finite Buffer ◽  
Queueing Model ◽  
Service Station ◽  
Matrix Geometric Method ◽  
In Series ◽  
Bulk Service ◽  
Number Of Customers

This paper analyses a queueing model consisting of two units I and II connected in series, separated by a finite buffer of size N. Unit I has only one exponential server capable of serving customers one at a time. Unit II consists of c parallel exponential servers and they serve customers in groups according to the bulk service rule. This rule admits each batch served to have not less than ‘a’ and not more than ‘b’ customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than ‘d’ ( a ≤ d ≤ b ). The steady stateprobability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained using the modified matrix-geometric method. Numerical results are also presented. AMS Subject Classification number: 60k25 and 65k30

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