acta satech Journal of the Life & Physical Sciences Babcock

On the application of steady state transition probability in g/m/1/k queueing system
*Agboola1, S. O. Ayinde2, S. A. and Karokatose3 G.
1Department of Mathematical and Computing Sciences, KolaDaisi University, Ibadan 2Department of Basic Science (Mathematics Unit), Babcock University, Ilisan Remo 3Department of Mathematics, Obafemi Awolowo University, Ile – Ife, Nigeria
October, 2019

ABSTRACT
We consider a general arrival and Markovian service time queueing system with one server under first come first served discipline, where the ij element of transition probability is given as matrix F and the system can accommodate finite number of arrival, K. Transition probability matrix and steady states probabilities were obtained. Numerical illustration is considered on D/M/1/5 queue, where the customers arrive at a rate of one per unit time and for which the mean of the exponential service time equals to 3/4 so as to reflect its usefulness in solving the real life problem. This gives the probability β_i, that i customers complete their service during the period k^th and (k+1)^th arrivals for β_i,i=0,1,2,⋯,5 as β_0 = 0.263597,β_1 = 0.351463, β_2 =0.234309,β_3 =0.104137,β_4 = 0.034712,β_5 = 0.009257 and its corresponding stationary probability π, of an arrival finding i customers already present as π = (0.473099,0.258124,0.14073,0.076003,0.038326,0.013719).
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