1. Queuing Theory Examples Problems
2. Applications Of Queuing Theory
3. Random Process And Queuing Theory Concepts
4. Queuing Theory Formula
5. Probability Random Processes And Queueing Theory Pdf

Because of random nature of the processes involved the queuing theory is rather demanding and all models are based on very strong assumptions (not always satisfied in practice). Many systems (especially queuing networks) are not soluble at all, so the only technique that may be applied is simulation. It considers the Poisson process, which is fundamental to computer science and to all the areas of applied probability. The birth-and-death process is a key element in queueing theory. The chapter discusses Markov chains. These are used in queueing theory and in many other computer science applications. Queueing Theory-8 Terminology and Notation. λ n = Mean arrival rate (expected # arrivals per unit time) of new customers when n customers are in the system. s = Number of servers (parallel service channels). µ n = Mean service rate for overall system (expected # customers completing service per unit time).

Figure 1 shows the elements of a single queue queuing system:

Population of Customers can be considered either limited (closed systems) or unlimited (open systems). Unlimited population represents a theoretical model of systems with a large number of possible customers (a bank on a busy street, a motorway petrol station). Example of a limited population may be a number of processes to be run (served) by a computer or a certain number of machines to be repaired by a service man. It is necessary to take the term 'customer' very generally. Customers may be people, machines of various nature, computer processes, telephone calls, etc.

Arrival defines the way customers enter the system. Mostly the arrivals are random with random intervals between two adjacent arrivals. Typically the arrival is described by a random distribution of intervals also called Arrival Pattern.

Queue represents a certain number of customers waiting for service (of course the queue may be empty). Typically the customer being served is considered not to be in the queue. Sometimes the customers form a queue literally (people waiting in a line for a bank teller). Sometimes the queue is an abstraction (planes waiting for a runway to land). There are two important properties of a queue: Maximum Size and Queuing Discipline.

Maximum Queue Size (also called System capacity) is the maximum number of customers that may wait in the queue (plus the one(s) being served). Queue is always limited, but some theoretical models assume an unlimited queue length. If the queue length is limited, some customers are forced to renounce without being served.

Queuing Discipline represents the way the queue is organised (rules of inserting and removing customers to/from the queue). There are these ways:

1) FIFO (First In First Out) also called FCFS (First Come First Serve) - orderly queue.

2) LIFO (Last In First Out) also called LCFS (Last Come First Serve) - stack.