International Science Community Association Research Journal of Mathematical and Statestical Sciences 2320 - 6047 2 10 2014 October 12 Approximate Analysis of A Single Server Queue with Unit Step Function 1 4 EN Dhanesh Garg 1 Department of Mathematics, Maharishi Markandeshwar University, Mullana-133203, INDIA > Research Paper 2014 7 24 2014 October 12 This study analyzed a single server queueing model with a time dependent arrival rate and service rate is constant. In this model, the incoming arrivals are Poisson stream, service times are negative exponentially distributed and the first come first served queueing discipline. We obtain an explicit expression for the state probability distribution with time dependent arrival rate using unit step function. For a special form of the traffic intensity, If the service rate is constant (= ), this corresponds to Copyright@ International Science Community Association