A single-channel queuing system has an average service time of 10 minutes and an average time between customer arrivals of 15 minutes. Service times and inter-arrival times both have exponential distributions. Find: a. customer arrival rate b. average number of customers in queue c. average time customers spend in the system

(a ) 4 per hour (b ) 4.5 minutes (c ) 3 minutes

Explanation:

Average time between customer arrival = 15 minutes

Average service time = 10 minutes

(a) To calculate the customer arrival rate

Arrival rate = 1 / time between Arrival

= 1 / 15

= 0.066 × 60

= 4 per hour

(b) To calculate the average number of customers in queue

( Arrival time )^2 / service time ( service time - Arrival time)

= (15)^2 / 10 ( 10 - 15)

= 225 / 10 (-5)

= 225 / 50

= 4.5 minutes

(c) To calculate the average time customers spend in the system

Arrival time / service time - Arrival time

= 15 / 10 - 15

= 15/ -5

= 3 minutes

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