A single volunteer octogenarian usher can scan tickets with a handheld device an

Question

A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.

How many theater patrons are waiting on their favorite octogenarian usher?

How busy is the octogenarian usher?

Explanation / Answer

Given are:

Arrival rate = a = 25 per hour

Service rate = s = 30 per hour

Thereforefore,

Utilization of the octagenerian ( How busy is the Octagenarian usher) = a/s 100 = 25/30 x 100 = 83.33 %

THE OCTAGENARIAN USHER IS BUYST 83.33% OF TOTAL TIME

Average number of theatre persons waiting

= a^2 / sx ( s -a ) = 25 x 25 / 30 x ( 30 - 25 ) = 25 x 25 / ( 30 x 5 ) = 4.166 ( 4.17 rounded to 2 decimal places )

AVERAGE 4.17 NUMBER OF THEATRE PERSONS WAITING ON THEIR FAVORITE OCTAGENARIAN USHER

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