A graphics reproduction firm has four automatic equipment units but occasionally becomes inoperative because of the need for supplies, maintenance, or repair. Each Unit requires service roughly twice each hour, or, more precisely, each Unit of equipment runs an average of 30 minutes before needing service. Service times vary widely, ranging from a simple service (such as pressing a restart switch or repositioning paper) to more detailed equipment disassembly. The average service time, however, is minutes. Equipment downtime results in a loss of $20 per hour. The one equipment attendant is Paid $6 per hour.
Using finite queuing analysis, answer the following questions:
B. What is the average number of units still in operation?
In lining framework, benefit time is characterized as the time required to serve a client.
Operation the complementary of standard benefit time is called cruel benefit rate and is represented as the number of clients served amid a settled time. In traditional terms, the benefit rate can be characterized as the capacity of the server or machine in the number of units per time.
The average number of Units in operation = Number of unit-down Unit
But down Unit = L+H
The formula becomes;
The average number of units in operation = Number of units-(L+H)
= 4 - (0.256+0.535)
The average number of Units in operation = 3.209
Benny the Barber owns a one-chair shop. At Barber College, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at the rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following:
c. The average time a customer is in the shop.
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