Single or Multiple Server Queuing Model

SINGLE/MULTIPLE SERVER QUEUE (Model 1 & 3) lambda/mu 1.333333333 s-1 1 Arrival rate 20 lambda/(mu*s) 0.666666667 Service rate 15 2.666666667 s factorial = 2 Number of servers 2 P(0) = 0.2 0.533333333 2 Utilization 66.67% n Pn 1 2 P(0), probability that the system is empty 0.2000 0 1 0.2 0.2 1 2 Lq, expected queue length 1.0667 1 1.333333333 0.266666667 0.266666667 1 2 Ls, expected number in system 2.4000 2 0 0.177777778 0 1 2 Wq, expected time in queue 0.0533 3 0 0.118518519 0 1 2 Ws, expected total time in system 0.1200 4 0 0.079012346 0 1 2 Probability that a customer waits 0.5333 5 0 0.052674897 0 1 2 6 0 0.035116598 0 1 2 7 0 0.023411065 0 1 2 8 0 0.015607377 0 1 2 9 0 0.010404918 0 1 2 10 0 0.006936612 0 1 2 11 0 0.004624408 0 1 2 12 0 0.003082939 0 1 2 13 0 0.002055292 0 1 2 14 0 0.001370195 0 1 2 15 0 0.000913463 0 1 2 16 0 0.000608976 0 1 2 17 0 0.000405984 0 1 2 18 0 0.000270656 0 1 2 19