QUEUING THEORY APPLICATIONS. Students arrive at the administrative service offic

Question

QUEUING THEORY APPLICATIONS. Students arrive at the administrative service office at an average rate of one every 15 minutes, and their requests take on the average 10 minute-to be processed the service counter is staffed by one clerk. gertrude High. who eight hours a day Assume Poisson arrivals and exponential service times,the computer output of this queuing system is found below. Time units are minutes. ADMINISTRATIVE OFFICE QUEUE I tM/M/C QUEUE STATISTICS (Time Unites: Minutes).Number of identical servers......... I Mean arrital rale............................0.0667 Mean service rale per server................0.1000 Mean server utilization (%)..................6.6667 Expected number of customers in queue....1.3333 Expected number of customers in system...2.0000 Probability that a customer must w ail....0.6667 Expected lime in the queue..................20.0000 Expected lime in the system..................30.0000

Explanation / Answer

(a) Percentage of the time Gertrude is idle=P( No students)= P(0)= 0.3333

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