Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008 1 EE 550: Problem Set # 8 Due: Monday, November 24, 2008 I. SLOTTED ALOHA WITH CAPTURE Book problem 4.7. II. SLOTTED CSMA Book problem 4.21. III. UNSLOTTED ALOHA Book problem 4.12. IV. SPLITTING ALGORITHMS Book problem 4.13(a)(b). V. MORE ON SPLITTING ALGORITHMS Book problem 4.15. VI. STABILIZING A SWITCH WITH UNIFORM TRAFFIC Consider an N × N packet switch with virtual input queueing. Suppose traffic arrives according to a continuous time Poisson process with uniform rates, so that λ ij = ρ/N for all input/output pairs ( i,j ) (for some value ρ < 1 ). Slot sizes are normalized to one unit of time. There are N ! possible permutation matrices M 1 ,M 2 ,...,M N ! . Consider the randomized scheduling policy of scheduling according to a randomly chosen permutation matrix (chosen with equal probability over all possible permutations). (a) For a single virtual input queue ( i,j ) , compute the probability that a server is allocated to this queue on a given slot. (b) Show that all virtual input queues are stable, and compute an exact expression for average delay (Hint: Use a slotted
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/21/2010 for the course EE 550 taught by Professor Neely during the Fall '08 term at USC.

Ask a homework question - tutors are online