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.

scholarly journals An M/M/1 Queue with Working Vacation and Vacation Interruption Under Bernoulli Schedule

2018 ◽  
Vol 7 (4.10) ◽  
pp. 448
Author(s):  
P. Manoharan ◽  
A. Ashok
Keyword(s):  
Geometric Approach ◽  
Stochastic Decomposition ◽  
Working Vacation ◽  
System Parameters ◽  
Mean Waiting Time ◽  
The Mean ◽  
Vacation Interruption ◽  
Mean Queue Length ◽  
Vacation Period ◽  
Bernoulli Schedule

This work deals with M/M/1 queue with Vacation and Vacation Interruption Under Bernoulli schedule. When there are no customers in the system, the server takes a classical vacation with probability p or a working vacation with probability 1-p, where . At the instants of service completion during the working vacation, either the server is supposed to interrupt the vacation and returns back to the non-vacation period with probability 1-q or the sever will carry on with the vacation with probability q. When the system is non empty after the end of vacation period, a new non vacation period begins. A matrix geometric approach is employed to obtain the stationary distribution for the mean queue length and the mean waiting time and their stochastic decomposition structures. Numerous graphical demonstrations are presented to show the effects of the system parameters on the performance measures.  

The Asymmetric PCF Control Technology of Gated Service Based on Continuous-Time

2013 ◽  
Vol 432 ◽  
pp. 582-586
Author(s):  
Guang Lan Zhao ◽  
Hong Wei Ding ◽  
Ying Ying Guo ◽  
Yi Fan Zhao ◽  
Ya Nan Hao
Keyword(s):  
Probability Generating Function ◽  
System Model ◽  
Embedded Markov Chain ◽  
Closed Expression ◽  
System Parameters ◽  
Mean Waiting Time ◽  
Defining System ◽  
The Mean ◽  
Mean Queue Length ◽  
And Performance

The paper starts with building system mathematical models and defining system parameters and working conditions to analyze the system model and performance, using the embedded Markov chain and probability generating function. The paper also deduces the accurate closed expression of the mean queue length and cycle time, gets approximate analysis expression of the mean waiting time well, and also verifies the correct theoretical analysis by simulation.

scholarly journals A queueing model for error control of partial buffer sharing in ATM

1999 ◽  
Vol 5 (4) ◽  
pp. 329-348
Author(s):  
Boo Yong Ahn ◽  
Ho Woo Lee
Keyword(s):  
Error Control ◽  
Approximation Scheme ◽  
Queueing System ◽  
Recursive Method ◽  
Loss Probabilities ◽  
Mean Waiting Time ◽  
System Equations ◽  
The Mean ◽  
Buffer Sharing

We model the error control of the partial buffer sharing of ATM by a queueing systemM1,M2/G/1/K+1with threshold and instantaneous Bernoulli feedback. We first derive the system equations and develop a recursive method to compute the loss probabilities at an arbitrary time epoch. We then build an approximation scheme to compute the mean waiting time of each class of cells. An algorithm is developed for finding the optimal threshold and queue capacity for a given quality of service.

Sign in / Sign up

Export Citation Format

Share Document