Quantitative Analysis Short Notes

Queueing Model: A Brief IntroductionLet us think about a queue (waiting line) most of us have seen, the line at Orins place caf in Paccar hall. Let us consider the simplest case, one line in front of a single cashi er. For now, ignore the role of second cashier (occasionally open) and the barista. We will discuss in class the wide applicability (not just cafes) of the insights we draw from this model. Inputs Customers arrive at the caf and join the line. The time between any two customer arrivals is variable and uncertain but we can say, for example, on average two customers join the line every minute. The rate at which customers join the line is what we call arrival rate (symbol lambda ). This is the same as workload arrival in chapter 1. In this case, arrival rate lambda is 2 per minute. This also means that the average time between two arrivals is minute; we call this interarrival time. The time cashier takes to serve one customer is called service time. This too cha nges from customer to customer and is, therefore, variable and uncertain. Let us say, on average, service time for a customer is