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Agboola, Sunday Olanrewaju

**keywords:** Transition probability matrix, Markovian service, general arrival, PASTA property

A general arrival and Markovian service time queueing system with one server under first come first served discipline was considered, where the ij element of transition probability is given as matrix F and the system can accommodates infinite number of arrival. The steady state transition probability were obtained and compared with the result from Markovian arrival and Markovian service times queueing system (M/M/1). The formulae for waiting time distribution, probability distribution and density functions for the response time (total system time) in a G/M/1 system were obtained. Illustrative numerical examples were demonstrated to shown its usefulness in solving the real life problem. We arrived at the following values for the root of equation of Z-transform of the number of service completions that occur during an interarrival period, ξ^j= 0.600, 0.6115, 0.6153, 0.6206, 0.6223, 0.6267, ⋯, Which is eventually converges to ξ=0.645705. Therefore, the probabilities that it contains zero, one or two customers are given, respectively by 0.4, 0.12 and 0.182. The probability that arrival find the system empty is 0.5, the mean number of customers seen by an arrival is 1.0 and the mean time spent waiting in this system is 0.2.

Agboola SO 2016. Repairman Problem with Multiple Batch Deterministic Repairs. Unpublished Ph.D. Mathematics (Statistics Option) Thesis submitted to Department of Mathematics, Obafemi Awolowo University, Ile-Ife. Agboola SO 2007. On the Analysis of M/G/1 Queues. Unpublished M.Sc. (Mathematics) Thesis submitted to Department of Mathematics, University of Ibadan. Agboola SO 2011. The Analysis of Markov Inter-arrival Queues Model with K – Server under Various Service Points. Unpublished M.Sc. (Statistics) Thesis submitted to Department of Mathematics, Obafemi Awolowo University, Ile-Ife. Bolch G, Greiner S & Trivedi KS 1998. Queueing Networks and Markov Chains. Wiley Interscience, New York. Jain M 2013. Transient analysis of machining system with service interruption, mixed standbys and priority. Int. J. Maths. Operations Res., 5(5): 604-625. Jain M & Singh M 2013. Bi-level control of degraded machining system with warm standby setup and vacation. Applied Mathematical Modelling, 28: 1015 - 1026. Kleinrock L 1975. Queueing systems, New York, pp. 60 - 158. Law AM & Kelton WD 2000. Simulation Modeling and Analysis. Third Edition, McGraw-Hill, New York. Lucantoni DM 1993. The BMAP/G/1 Queue: Models and Techniques for performance evaluation of computer and communications systems. Springer. Medhi J 1980. Stochastic Application of Queuing Theory. Guahandi University, Guwa-hata, Indian, pp. 23 - 120. Meini B 1997. New convergence results on functional techniques for the numerical solution of M/G/1 Type Markov Chains. Numer. Math., 78: 39-58. Ross SM 1997. Simulation. Second edition, Academic Press, New York. Saad Y 2003. Iterative Methods for Sparse Linear Systems. Second edition, SIAM Publications, Philadelphia. William Stewart 2009. Probability, Markov Chains, Queueing and Simulation, Princeton University Press, Princeton and Oxford.