6%20-%20Network%20of%20Queues

6%20-%20Network%20of%20Queues - Probability and Random...

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Probability and Random Processes STA 3533 Module 6 Networks of Queues

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Topics Introduction to queuing (waiting line) theory Open queuing networks Closed queuing networks General service distribution and multiple job types Response time distribution computation
Gain terminology, classifications and methods of waiting lines Learn fundamental principles, generalizations and theories of the study of waiting Develop waiting line competencies needed by E.C.E professionals Objectives

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1 Introduction to Queuing
Introduction to Queuing Basic Process Customers requiring service are generated over time by an input source Customers enter the queuing system and enter a queue At certain times, a member in the queue is selected for service by some rule known as the queue discipline Required service then performed for the customer by the service mechanism , after which the customer leaves the queuing system.

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Input Source Size of input source is the total number of customers that might require service from time to time (total number of distinct potential customers) Population from which arrivals come is the Calling Population Can be finite or infinite Thus, input source is said to be limited or unlimited Assume infinite even when finite (relatively large number) because mathematics are easier Finite more difficult because number of customers in system and rate of service affects the size of the waiting line Introduction to Queuing
Input Source Number of customers until any specific time ( arrivals ) generated according to Poisson distribution Consequently, time between consecutive arrivals ( inter-arrival time ) is exponential. Introduction to Queuing

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Introduction to Queuing Queue examples: Customer waiting in the line to be served by the bank representative at the bank. Caller waiting for the phone call to be connected to the receiver while the network is busy. Customer waiting at the phone call for getting service from customer care representative at mobile service provider. Message waiting at the router in the network to be route to the next router. Digital signal waiting at the converter to be converted to the Analog signal at receiver side in communication system.
Elements of Queuing System N(t) – Number in the system N q (t) – Number in the Queue N s (t) – Number in the service W – Waiting time in the Queue τ – Service time T – Total time in the system Introduction to Queuing Server 1 Server 1 Server 2 Server 2 Server c Server c System System N(t) N q (t) (t) W T N s (t) (t)

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Now lets understand the above system elements.
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This note was uploaded on 06/14/2011 for the course HIST 1301 taught by Professor Gonzales during the Spring '11 term at The University of Texas at San Antonio- San Antonio.

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6%20-%20Network%20of%20Queues - Probability and Random...

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