An important measure of effectiveness is the probability that an arriving customer has to wait. This...

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An important measure of effectiveness is the probability that an arriving customer has to wait. This quantity is often referred to as the delay probability and denoted by w. For an M/M/c queueing model, derive the relationship between w and the average queue size and wait, L, and W, by showing the following: (a) Pe+n = ppc (b) w La (d) Wa = = = Pc 1-P (Hint: Use part (a).) P 1 (Hint: Use the fact that n=c+1 (n - c)pn (e) How does w relate to C(c, r)? = npetn.) An important measure of effectiveness is the probability that an arriving customer has to wait. This quantity is often referred to as the delay probability and denoted by w. For an M/M/c queueing model, derive the relationship between w and the average queue size and wait, L, and W, by showing the following: (a) Pe+n = ppc (b) w La (d) Wa = = = Pc 1-P (Hint: Use part (a).) P 1 (Hint: Use the fact that n=c+1 (n - c)pn (e) How does w relate to C(c, r)? = npetn.)