notes09 - Network of Queues TELCOM 2120 Network Performance...

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1 Network of Queues TELCOM 2120 Network Performance Joseph Kabara Telecommunications Program University of Pittsburgh Spring 2008, notes9 TELCOM 2120: Network Performance 2 Network of Queues Many communication systems must be modeled as a set of interconnected queues – which is termed a queueing network. Systems modeled by queueing networks can be grouped into four broad categories – Open networks – Networks with population constraints – Closed networks – Mixed network Spring 2008, notes9 TELCOM 2120: Network Performance 3 Open Networks Customers arrive from outside the system are served and then depart. Example: Packet switched data network. 1 γ 1 μ 2 3 2 3
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2 Spring 2008, notes9 TELCOM 2120: Network Performance 4 Networks with Population Constraints Customers arrive from outside the system if there is room in the queues. They enter, served and then depart. Example: queues sharing a common buffer pool. γ 1 μ 2 3 Spring 2008, notes9 TELCOM 2120: Network Performance 5 Closed Networks Fixed number of customers ( K ) are trapped in the system and circulate among the queues. Example: CPU job scheduling problem 1 2 k Spring 2008, notes9 TELCOM 2120: Network Performance 6 Mixed Network Any combination of previous types. Example: simple model of virtual circuit that is window flow controlled. 1 2 k
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3 Spring 2008, notes9 TELCOM 2120: Network Performance 7 Properties in Queueing Networks Jocking Customers moving among parallel queues. Blocking Customer waiting depart a server and join next queue is unable to due to limited waiting space, and therefore stays in server (blocking it.) Forking Customer leaving a queue clones into multiple customers going along different routes. Joining Multiple streams of customers are combined into a single stream. Forking and joining are used in models of parallel processing systems. Spring 2008, notes9 TELCOM 2120: Network Performance 8 Open Networks • The simplest type of network is an open network with the following assumptions (called Jackson Network ) – which amount to each queue being a M/M/1 type – Assume arbitrary network of M queues. – Service time of queue i is exponentially distributed with rate . – Arrivals from outside the network to queue i are a Poisson process with mean rate . i μ i γ Spring 2008, notes9 TELCOM 2120: Network Performance 9 Open Networks (2) routing probability that a customer completing service at queue i goes to queue j . routing probability that a customer completing service at queue i leaves the network. i i r 1 1 λ i r 2 2 mi m r i i i 1 i r 2 i r im r ) 1 ( + m i ii r j i r , j i r , 1 , + m i r
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4 Spring 2008, notes9 TELCOM 2120: Network Performance 10 Open Networks (3) Let be the total mean customer arrival rate to queue i .
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notes09 - Network of Queues TELCOM 2120 Network Performance...

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