A teller at Kiti savings and credit society can serve an average of one customer in

every 3 minutes. On average, a customer arrives after every 4 minutes.

Using the simple queuing model, determine the:

(i) average number of customers in the queue;

(ii) | average number of customers in the queuing system;

(iii) | average time a customer spends in the system.(8 marks)November 2022

The simple queuing model uses a formula known as the Erlang-C formula to calculate the average number of customers in the queue, the average number of customers in the queuing system, and the average time a customer spends in the system.

(i) The average number of customers in the queue can be calculated by dividing the arrival rate (λ) by the departure rate (µ) and subtracting 1. λ/µ – 1 = (1/4) / (1/3) – 1 = 0.25

(ii) The average number of customers in the queuing system can be calculated by dividing the arrival rate (λ) by the departure rate (µ) and multiplying by the traffic intensity (rho) which is the ratio of arrival rate to departure rate. λ/(µ(µ-λ)) = (1/4) / (1/3) * (1/4) = 0.33

(iii) The average time a customer spends in the system can be calculated by dividing the average number of customers in the system by the arrival rate (λ). Ls = Ws + 1/µ = 0.33 + 1/3 = 0.44

In conclusion: