final_2006

final_2006 - MS&E 221 Ramesh Johari Final Examination...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Final Examination Ramesh Johari March 22, 2006 Instructions 1. Take alternate seating if possible. 2. Answer all questions in the spaces provided on these sheets. If needed, additional paper will be avail- able at the front of the room. Answers given on any other paper will not be counted. 3. You may use no notes, books, or calculators. 4. Explain your answers! It helps earn you partial credit. 5. The examination begins at 8:30 am, and ends at 11:30 am. Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1. If T is an exponentially distributed random variable with mean 1 , then the density of T is given by f T , where: f T ( t ) = λe - λt , t 0 . 2. If S is a random variable with a gamma distribution of parameters n and λ , where n is a positive integer, then the density of S is given by f S , where: f S ( s ) = λe - λs ( λs ) n - 1 ( n - 1)! , s 0 . 3. For an M/M/ 1 queue with arrival rate λ and service rate μ with λ < μ , the equilibrium distribution is: P ( Q = j ) = (1 - ρ ) ρ j , j = 0 , 1 , 2 ,..., where ρ = λ/μ . 4. For an M/M/ queue with arrival rate λ and service rate μ , the equilibrium distribution is: P ( Q = j ) = e - ρ ρ j j ! , j = 0 , 1 , 2 ,..., where ρ = λ/μ . 5. For an M/M/K/K queue with arrival rate λ and service rate μ , the equilibrium distribution is: P ( Q = j ) = ρ j /j ! 1 + ··· + ρ K /K ! , j = 0 , 1 , 2 ,...,K, where ρ = λ/μ . 2
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/03/2011 for the course MS&E 221 taught by Professor Ramesh during the Winter '11 term at Stanford.

Page1 / 12

final_2006 - MS&amp;E 221 Ramesh Johari Final Examination...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online