FORM_FIN - ENSC 427 Final Exam FORMULA SHEET 2007 Notation:...

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ENSC 427 FORMULA SHEET 2007 Final Exam Notation: Steady-state probability of having n packets in the system Arrival rate (inverse of average interarrival time) Service rate (inverse of average service time) E ( n ) = Average number of packets in the system E ( q ) = Average number of packets waiting in queue E ( T ) = Average packet time in the system E ( w ) = Average packet waiting time in queue (does not include service time) Average service time Second moment of service time Little’s formula: For systems with blocking, Poisson distribution with parameter λ : Mean = Variance = λ Exponential distribution with parameter μ : p n = λ= μ= X = X 2 = E ( n )=λ E ( T ) E ( q E ( w ) E ( n )=λ( 1 P B ) E ( T ) E ( q 1 P B ) E ( w ) p n = e −λ λ n n ! , n = 0 , 1 ,… P {τ ≤ s }= 1 e −μ s , s 0 Density: p (τ) = μ e −μτ Mean = 1 μ Variance = 1 μ 2 - 1 -
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Summary of M/M/1/ system results: 1. Utilization factor (proportion of time the server is busy) 2. Probability of n packets in the system 3. Average number of packets in the system 4. Average packet time in the system 5. Average number of packets in buffer 6.
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This note was uploaded on 10/09/2009 for the course ENSC 1156 taught by Professor Rhardy during the Spring '07 term at Simon Fraser.

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FORM_FIN - ENSC 427 Final Exam FORMULA SHEET 2007 Notation:...

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