A.compute how many items are waiting or being serviced in a process that has an

Question

A.compute how many items are waiting or being serviced in a process that has an arrival rate of 1,746 units per hour and a service rate of 2,382 units per hour.

Round to the nearest one decimal place.
Put only the numeric portion of your answer in the first blank.
Units may optionally be put in the second blank.

B. compute the intensity of a process that has an arrival rate of 1,561 units per hour and a service rate of 2,790 units per hour.

Give answer as a percent (yes, you'll need to think a little). Round to the nearest one decimal place.
Put only the numeric portion of your answer in the first blank.
Units may optionally be put in the second blank.

C. assume an initial arrival rate of 1,650 units per hour and a service rate of 2,039 units per hour. Use Goal Seek to determine the arrival rate necessary for 1.3 items waiting or being processed.

Round to the nearest one decimal place.
Put only the numeric portion of your answer in the first blank.
Units may optionally be put in the second blank.

Explanation / Answer

Assuming this to be the simplest of queue that is M/M/1.

A. Rho = 1746/2382 =0.7329

Avg. number of units in the system = rho /1-rho = 0.7329 / 0.2670 = 2.744

Avg number of units in the queue =( rho)2 /1-rho = 2.011

B.

Intensity of process = rho = 1561/2790 = 0.5591 = 55.91% = 56%

C. For 1.3 items waiting in queue

1.3 =(rho)2 / 1-rho

which gives the equation

1.3-1.3rho = (rho)2

gives the value of rho as 0.6624

Necessary arrival rate for a service rate of 2039 units per hour

0.6624 = lambda / 2039 which gives lambda = 1363.88 = 1369

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