An arrival distribution for the equilibrium expected waiting time in a discrete-time single-server queue with acceptance period and Poisson population of customers
This study considers a discrete-time first-come first-served single-server queue with acceptance period. Customers arrive at the system within the acceptance period. The total number of arriving customers is Poisson distributed, and their service times are independent and identically distributed with a general distribution. It is assumed that each customer chooses its arrival time slot with the goal of minimizing its expected waiting time.
For this queueing model, we obtain an arrival distribution of customers for the equilibrium expected waiting time, called an equilibrium arrival distribution for short. Through some numerical examples, we show that the large variation of service times causes the rush of customers to the opening slot. Furthermore, we propose a simulation model which will exhibit an arrival time distribution similar to the one in equilibrium.