There is only one copying machine in the student lounge of the business school.

Question

There is only one copying machine in the student lounge of the business school. Students arrive at the rate of 40 per hour (according to a Poi son d tribution). Copying takes an average of 45 seconds or ?·80 per hour (according to a negative exponer tal dstrbtin) a) The percentage of time the machine is used " ? percent round your response to the nearest whle numb e). b) The average length of the queue students (round your response to two decimal places c) The average number of students in the systom students (round your rosponse to two decimal places d) The average time spent waliting in the queue minutos (round your response to two decimal places) e) The average time in the system minutes (round your response to two decimal places)

Explanation / Answer

Following details are provided :

Arrival rate of students = a = 40 per hour

Service rate by copying machine = s = 80 per hour

= a^2/S x ( S -a )

= 40 x 40 / 80 x ( 80 – 40 )

= 40 x 40 / ( 80 x 40 )

= 1/ 2

= 0.50

= Average length of the queue + a/ s

= 0.5 + 40/80

= 0.5 + 0.50

= 1

= a/ S x ( s – a ) hour

= 40 / 80 x ( 80 – 40 )

= 40/ 80 x 40

= 1/ 80 hours

= 60/80 minutes

=0.75 minutes

= Average time waiting in the queue + 1/ Shours

= 1/80 + 1/80 hours

= 2/ 80 hours

= 1/40 hours

= 60/40 minutes

= 1.5 minutes

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