FORM_MT - ENSC 427 Mid-Term Exam FORMULA SHEET 2007...

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ENSC 427 FORMULA SHEET 2007 Mid-Term 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 )=λ E ( w ) E ( n )=λ( 1 P B ) E ( T ) E ( q )=λ( 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)
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FORM_MT - ENSC 427 Mid-Term Exam FORMULA SHEET 2007...

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