Indexing
All Issues
Submission
Author Guidelines
Reviewers
Editorial Members
Publication Fee
Vol.3 , No. 5, Publication Date: Sep. 26, 2017, Page: 32-46
. While serving the customer, we assume interruptions arrive at random according to a Poisson process with mean rate αand βbe the rate of attending interruption. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a random setup time process. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also the average number of customer in the queue and the average waiting time are derived. Numerical results are computed.&picture=http://www.aascit.org/aascit/decorators/img/journal/928.jpg)
| [1] | Govindan Ayyappan, Department of Mathematics, Pondicherry Engineering College, Puducherry, India. |
| [2] | Pakiradhan Thamizhselvi, Department of Mathematics, Pondicherry Engineering College, Puducherry, India. |
| [3] | Karuppannan Sathiya, Department of Mathematics, Rajiv Gandhi Govt Arts College, Puducherry, India. |
This paper deals with the study of batch arrival queue with a single server providing three stages of heterogeneous service, subject to random interruption and vacation. As soon as the completion of third stage service, if the customer is dissatisfied with its service, he can immediately join the tail of the original queue as a feedback customer. After completion of the three stages of service in succession to each customer the server has the option to take a vacation of random length with probability θ or to continue staying in system with probability (1-θ). While serving the customer, we assume interruptions arrive at random according to a Poisson process with mean rate αand βbe the rate of attending interruption. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a random setup time process. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also the average number of customer in the queue and the average waiting time are derived. Numerical results are computed.
Keywords
Batch Arrival, Service Interruption, Bernoulli Vacation, Setup Time, Transient Solution, Average Queue Size, Average Waiting Time
Reference
| [01] | Ayyappan. G and Shyamala. S, M[X]/G1, G2/1 with setup time, Bernoulli vacation, Breakdown, and DelayedRepair, International Journal ofStochastic Analysis, (2014). |
| [02] | Chae, K. C. Lee, H. W. and Ahn, C. W. An arrival time approach to M/G/1 type queues with generalisedvacations, Queueing Systems, (2001) vol. 38, pp. 91-100. |
| [03] | Choudhury. G, An M[X]/G/1 queueing system with a setup periodand a vacation period, QueueingSystems, (2000) vol. 36, pp. 23-38. |
| [04] | Choudhury. G, A note on the M[X]/G/1 queue with a random set-up time under a restricted admissibility policywith a Bernoullischedule vacation, Statistical Methodology, (2008) vol. 5, pp. 21-29. |
| [05] | Doshi, B. T., Queueing systems with vacation-a survey, Queueing Systems, (1986) vol. 1, No. 1, pp. 29-66. |
| [06] | Gross. C and Harris. C. M, The fundamentals of queuing theory, (1985) second ed., John Wiley and Sons, New York. |
| [07] | Kashyap. B. R. K, Chaudhry. M. L, An introduction to queuing theory, A and A publications, Kingston, Ont., Canada (1988). |
| [08] | Madan. K. C, Choudhury. G, An M[X]/G/1 queue with a Bernoulli schedule vacation under restrictedadmissibility policy, Sankhya, (2004) vol. 66, no: 1, pp. 175-193. |
| [09] | Madan. K. C and Rawwash. M. A, On the M[X]/G/1 queue withfeedback and optional server vacationsbased on a single vacation policy, Applied Mathematics and Computation, (2005) vol. 160, pp. 909-919. |
| [10] | Maragatha Sundari. S and Srinivasan. S, Time dependent solution of a Non-Morkovian queue with triple stagesof services having compulsory vacation and service intereptions, International Journal of Computer Applications, (2012) Vol. 41, No. 7, pp. (0975-8887). |
| [11] | Maragathasundari, S., Karthikeyan, K. Batch Arrival Of Two Stages With Standby ServerDuring General Vacation Time & General Repair Time International Journal of Mathematical Archive (2015a), Vol. 6 (4), pp. 43-48. |
| [12] | Maragathasundari, S. and Karthikeyan, K. A Study on M/G/1 Queueing System with ExtendedVacation, Random Breakdowns and General Repair International Journal of Mathematics And its Applications (2015b), Vol. 3, pp. 43-49. |
| [13] | Medhi. J, Stochastic Processes, Wiley, Eastern (1982). |
| [14] | Rehab F. Khalaf, Kailash C. Madan and Cormac A. Lukas AnM[X]/G/1 queue with Bernoulli schedulegeneral vacation times, general extended vacations, random breakdowns, general delay times for repairs to start andgeneral repair times, Journal of MathematicsResearch, (2011) Vol. 3, no. 4. |
| [15] | Takagi, H. Time - dependent analysis of an M/G/1 vacation models with exhaustive service, QueueingSystems, (1990) vol. 6, No. 1, pp. 369-390. |
| [16] | Thangaraj. V and Vanitha. S, A single server M/G/1 feedback queue with two types of service having generaldistribution, International Mathematical Forum, (2010a) vol. 5, no. 1, pp. 15-33. |
| [17] | Thangaraj. V and Vanitha. S An M/G/1 queue with two-stage heterogeneous service compulsory servervacation and random breakdowns, Int. J. Contemp. Math. Sciences, (2010b) Vol. 5, no. 7, pp. 307-322. |
