TAILIEUCHUNG - Lecture Networking theory & fundamentals - Chapter 8

The following will be discussed in this chapter: Closed jackson networks, convolution algorithm, calculating the throughput in a closed network, arrival theorem for closed networks, mean-value analysis, norton’s equivalent. | Lecture Networking theory & fundamentals - Chapter 8 TCOM 501: Networking Theory & Fundamentals Lecture 8 March 19, 2003 Prof. Yannis A. Korilis 1 8-2 Topics Closed Jackson Networks Convolution Algorithm Calculating the Throughput in a Closed Network Arrival Theorem for Closed Networks Mean-Value Analysis Norton’s Equivalent 8-3 Closed Jackson Networks µ1 µ2 λ1 λ2 r51 µ5 λ5 r53 λ3 µ3 λ4 µ4 M Closed Network: K nodes with exponential servers No external arrivals (γi=0) , no departures (ri0=0) Fixed number M of circulating customers Appropriate model for systems with “limited” resources, ., flow control mechanisms Steady-state distribution will be shown to be of “product-form” type 8-4 Closed Jackson Network µ1 µ2 λ1 λ2 Aggregate arrival rates r51 λ5 µ5 λi = ∑ j =1 λ j rji , i = 1,., K K r53 Relative arrival rates – visit ratios λ3 µ3 λ4 µ4 M Can only be determined up to a constant Use an additional equation to obtain unique solution to the above system, . Set λ =1, for some node j j Set λ =µ , for some node j j j Set λ + λ + + λ =1 1 2 K ni: number of customers at node i Possible states for the closed network n=(n1, n2, ,nK), with ni ≥ 0 and

• Quản trị mạng
• Networking theory
• Queueing Theory
• Lecture Networking theory
• Closed jackson networks
• Convolution algorithm
• Arrival theorem for closed networks
• Packet networks
• Probability theory
• The poisson process
• Little’s Theorem
• Markov Chains
• Discrete time markov chains
• Global balance equations
• Sojourn Times
• Time Averages
• Time reversal of Markov Chains
• Reversible markov chain
• Open jackson networks
• Network flows
• State dependent service rates
• Pollaczek khinchin formula
• Embedded markov chain
• Priority queueing
• Routing in data network
• Graph representation of a network
• Undirected graphs
• Processing delay
• Delay models
• Network layer
• Propagation delay
• Transmission delay
• Queueing delay
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