Queueing-Stimulation

This queueing system consists of one or more queues of elements waiting to be served by one or more servers. When an element is removed from the front of a queue, a server serves that element. How queues and servers interact and parameters such as the numbers of queues and servers, how often new elements arrive, and how often servers remove elements from queues determine the behavior of a queueing system. This program simulates a queueing system. A probabilistic simulation calls a pseudo-random number generator to determine if events occur, and their parameters, at each tick of the simulation's clock. This program is a probabilistic simulation of a queueing system with several queues and several servers, one server for each queue, as in a grocery or discount store. Because there are several lines, each arriving customer always joins the line that is currently the shortest. If several lines are equally short, the new arrival may join any one of them. A line with a free teller is "shorter" than one whose teller is occupied. Once in a line, a customer does not leave it until served. The program reads from the terminal the parameters of the simulation---how many queue/server pairs, the longest time for a transaction, the probability that a customer arrives during a single tick, the duration of the simulation---and a seed value for the random number generator. It simulates the queueing system for the specified duration, showing a picture of the system at every clock tick, then reports some statistics: the average time each customer waited, the longest time any customer waited, the number of customers served, and the numbers of customers left in queues. The number of queue/server pairs, of course, is at least 1. The probability that a customer arrives during one tick is a percentage, thus an integer between 0 and 100. Each transaction's time is random, uniformly distributed between one tick and a positive maximum value entered from the terminal.