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EEL6507 Spring 2009, Lecture 01, Wednesday 2008/01/07 (Notes created by O. Boykin)

Covered an introduction to the syllabus. See the course website for more information.

Introduction to Queueing Model

Our model of a queue is a stochastic model where we are given an arrival pattern, service pattern, number of servers, queue capacity and queue discipline. There are customers that come to the server for service. They join the queue. A server takes a single customer from the queue to provide service. The system is the queue and the servers.

Arrival Pattern: The arrival pattern is the CDF for the arrival time: $A(t) = Prob[\text{arrival in time} \le t]$ . So, each inter-arrival time is an independent random variable.
Service Pattern: The service pattern is the CDF for the arrival time: $B(t) = Prob[\text{service in time} \le t]$ . So, each service time is an independent random variable.
Number of Servers: In our simple queue model, we will allow any integer number of parallel servers which can each serve the queue.
Queue Capacity: the maximum number of customers that the queue can hold before customers must be turned away.
Queue Discipline: the order in which customers are served. Usually we consider first-come-first-serve. Some examples:
- FCFS: First come first serve
- LCFS: Last come first serve (LIFO), this is like a stack
- RSS: Random service selection
- Priority: the highest priority customer is served next