Suppose that there are an infinite number of servers in the

Suppose that there are an infinite number of servers in the queueing system M/M/ infinity. Suppose that the arrival rate is alpha and the service rate for each server is . Determine the steady-state probabilities for this system. In Gambler\'s Ruin two players engage in a game of chance in which A wins a dollar from B with probability p and B wins a dollar from A with probability q = 1 - p. There are N dollars between A and B and A begins the n dollars. They continue to play the game until A or B has won all of the money. What is the probability that A will end up with all the money assuming that p > q. Assume that p = which happens to be the house advantage in roulette. What is the probability that A will win all the money if n = $100 and N = $1, 000,000,000?

Solution

Problem 8:

Using Bayes Law:

Required probability:

{1/2*5/12}/[{1/2*5/12}+{1/2*8/11}]={5/24}/{5/24+8/22}=110/302=55/151