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Unformatted text preview: Computer Networks A gentle introduction to queuing theory Saad Mneimneh Computer Science Hunter College of CUNY New York So how little is Littles theorem? 1 Introduction Before we address other aspects of TCP or start discussing the network layer, we consider some theoretical treatment of the network as a system that provides service to customers. In this system, customers arrive at random times to obtain service. system customers Figure 1: Customers arrive to the system for service In the context of computer networks, customers represent packets (or frames, and we shall not make the distinction here), and service represents the assignment of packets to communication links. For instance, if a link (server) has a bandwidth of B bps (service rate), then the service time for a packet (customer) assigned to that link will be L/B , where L is the size of the packet in bits (including headers if frame). Because the number of servers is usually finite, customers of this system are often modeled to be waiting for service in queues. Queuing theory is the field responsible for the study of such systems. The theory will help us gain some insight about buffer space, packet delays, and network utilization. This in turn could help us in the design of switching strategies (network layer) and congestion control mechanisms (e.g. TCP). 1 We are interested in answering questions like: What is the average number of customers in the system? (i.e. the typical number waiting in queue or undergoing service) What is the average delay per customer? (i.e. the typical time a customer waits in queue plus the service time) These quantities are often obtained in terms of known information such as: The customer arrival rate (i.e. the typical number of customers entering the system per unit time) The customer service rate (i.e. the typical number of customers the system serves per unit time when it is constantly busy) 2 Preliminaries Let us work out what we mean by average or typical. We start with few definitions: N ( t ) = Number of customers in the system at time t A ( t ) = Number of customers who arrive in the interval [0 ,t ] T i = Time spent in the system by the...
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- Spring '08
- Computer Networks