Consider an M/M/ type queue (in the sense that there is no limit on the number...

 

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Consider an M/M/ type queue (in the sense that there is no limit on the number of servers) with variable arrival and service rates Ak = (k+2)A Pk = kp (k 0) (k 1). (a) Derive a closed form expression for the steady state probabilities p,, that only depends on n and p= (b) Find the mean number in the system at steady state L. This should be a closed form expression in p. Consider an M/M/ type queue (in the sense that there is no limit on the number of servers) with variable arrival and service rates Ak = (k+2)A Pk = kp (k 0) (k 1). (a) Derive a closed form expression for the steady state probabilities p,, that only depends on n and p= (b) Find the mean number in the system at steady state L. This should be a closed form expression in p.