Analysis of MAP/PH_{1}^{E}, PH_{2}^{O} /1 Queue with Standby Server, Second Optional service, Variant arrival rate, Bernoulli Schedule Vacation, Impatient Behavior of Customers, Breakdown, Essential and Optional Repair

2021 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
AYYAPPAN Govindan ◽  
Thilagavathy Karthikeyan
Keyword(s):  
Arrival Rate ◽  
Optional Service ◽  
Second Optional Service ◽  
Bernoulli Schedule

scholarly journals Transient Solution of M[X]=G=1 With Second Optional Service, Bernoulli Schedule Server Vacation and Random Break Downs

2013 ◽  
Vol 3 (3) ◽  
pp. 45-55
Author(s):  
S. SHYAMALA ◽  
Dr. G. AYYAPPAN
Keyword(s):  
Arbitrary Distribution ◽  
Breakdown Rate ◽  
Mean Waiting Time ◽  
Optional Service ◽  
Second Optional Service ◽  
Poisson Stream ◽  
The Mean ◽  
Mean Queue Length ◽  
Bernoulli Schedule ◽  
Essential Service

In this model, we present a batch arrival non- Markovian queueingmodel with second optional service, subject to random break downs andBernoulli vacation. Batches arrive in Poisson stream with mean arrivalrate (> 0), such that all customers demand the rst `essential' ser-vice, wherein only some of them demand the second `optional' service.The service times of the both rst essential service and the second op-tional service are assumed to follow general (arbitrary) distribution withdistribution function B1(v) and B2(v) respectively. The server may un-dergo breakdowns which occur according to Poisson process with breakdown rate . Once the system encounter break downs it enters the re-pair process and the repair time is followed by exponential distributionwith repair rate . Also the sever may opt for a vacation accordingto Bernoulli schedule. The vacation time follows general (arbitrary)distribution with distribution function v(s). The time-dependent prob-ability generating functions have been obtained in terms of their Laplacetransforms and the corresponding steady state results have been derivedexplicitly. Also the mean queue length and the mean waiting time havebeen found explicitly.

scholarly journals Transient solution of /G/1 with Second Optional Service Subject to Reneging during Vacation and Breakdown time

2015 ◽  
Vol 3 (1) ◽  
pp. 206-213
Author(s):  
Suganya S Vijay
Keyword(s):  
Arrival Rate ◽  
Queuing Model ◽  
Breakdown Time ◽  
Mean Waiting Time ◽  
Optional Service ◽  
Second Optional Service ◽  
Poisson Stream ◽  
The Mean ◽  
System Breakdown ◽  
Mean Queue Length

In this paper, we present a batch arrival non- Markovian queuing model with second optional service. Batches arrive in Poisson stream with mean arrival rate ?, such that all customers demand the first essential service, whereas only some of them demand the second "optional" service. We consider reneging to occur when the server is unavailable during the system breakdown or vacations periods. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.

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