Find P N while using the transition diagram Arrival are Poisson with rate X. There are

Find P_N  while using the transition diagram

  

Transcribed Image Text:

Arrival are Poisson with rate X. There are c servers. Each has an independently and identically distributed (iid) exponential service-time distribution with mean ¹. λ 3μ Number in System Figure 2.6 Rate transition diagram for the M/M/e queue. Using a result of birth-death process developed earlier, the probability of n in the system is given by Pn= n! Po, An - Po 0<n<c. c≤n. Arrival are Poisson with rate X. There are c servers. Each has an independently and identically distributed (iid) exponential service-time distribution with mean ¹. λ 3μ Number in System Figure 2.6 Rate transition diagram for the M/M/e queue. Using a result of birth-death process developed earlier, the probability of n in the system is given by Pn= n! Po, An - Po 0<n<c. c≤n.