Open Access Open Access  Restricted Access Subscription or Fee Access

A Study on Time Dependent Solution of Single Server Queue with Markovian Arrival and Markovian Service

S. Shanmugasundaram, A. Shanmugavadivu


A M / M / 1 Queueing model with time dependent solution for single server queuing model with Markovian arrival and Markovian service time for busy period is derived and we find the various probabilities of number of units present in the system  and number of units leave the system at that  instant  t  during the busy period using the difference and difference equation technique.  The numercial study for various aspects are discussed.


Busy Period, Co-Efficient of Variance, Markovian Distribution, Mean, Moments, Pn(t), qn(t), Transient State, Variance.

Full Text:



Erlong,A.K, The theory of probabilitiesand telephone conversations,Nyt Jindsskriff Mathematic, B 20,33-39 (1909).

Faramand,K, A Single line queue with repeated demands, Queueing Systems, 6,223-228 (1990).

Fayolle,G., A simple telephone exchange with delayed feedbacks, eds.O.J.Boxma, J.W.Coheu and H.C.Tijms, Elsevier Teletraffic Analysis and Computer Performance Evolution (1986).

Krishna Kumar B., Arnambi D. (2000) Transient solution of an M/M/1 queue with catastrophes. Computers and Mathematics with Applications, 40, 1233-1240.

P.R Parthasarathy, A transient solution to an M/M/1 queue, A imple approach. (Adv Appl. Prob. 19, 997-998 (1987))

Santhakumaran, A., and Thangaraj,V., A single server queue with impatient and feedback customers, International Journal of Information and Management Sciences,

Santhakumaran, A., and Shangasundaram, S., Preparatory work on arrival customers with a single server feedback queue. International Journal of Information and Management Sciences, 19(2), (June 2008 accepted for publication).

Santhakumaran, A., and Shangasundaram, S., A single server retrial queue with Bernoulli schedule and instantaneous feedback, (Communicated for publication 2007).A simple approach, Journal of Applied Probability, 26 (1986), 584{594.

Sudesh Pal - equilibrium behavior in a single server observed queue.

Takacs,L, A Single Server Queue with feedback, The Bell System Technical Journal, 42,505-519 (1963).

Stochastic Process , J. Medhi, Second edition.

Stochastic Models in Queueing Theory, J. Medhi, Second edition.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.