HP 12c Solutions Handbook

Also see for 12C: User guide Reference guide User guide Quick start guide Specifications

Contents

144Richard E Trueman, "An Introduction to Quantitative Methods for DecisionMaking," Holt, Rinehart and Winston, New York, 1977Example 1: Bank customers arrive at a bank on an average of 1.2customers per minute. They join a common queue for three tellers. Eachteller completes a transaction at the rate of one customer every 2 minutes(0.5 customers per minute). What is the average waiting time in thequeue? In the system? What is the average number of customers in thequeue? In the system?From Table 12.2, page 512 of the reference, the mean waiting time as amultiple of mean service time for n = 3, ρ/n = 0.8 is 1.079. (Note S is usedinstead of n in the reference's notation).If the number of servers is limited to one, with other conditions remainingthe same (unlimited queue, Poisson arrival, exponential service), theaverage queue length can be readily calculated without reference to tables:1. Key in the arrival rate, λ, and press 1.2. Key in the service rate, μ, and press 2 21 to calculate the average number ofcustomers waiting in queue at any one time.3. Press 1 to calculate the average waiting time.4. Press 2 to calculate the average total time the customerspends in the system.5. Press 1 to calculate the average number of customers in thesystem.Example 2: A small grocery store has but a single check-out counter.Customers arrive at a rate of 1 every 2 minutes (λ = .5) and, on theaverage, customers can be checked out at a rate of .9 per minute (μ).Keystrokes Display1.2 1.20.5 2.40 ρ, intensity factor.3 0.80 ρ / n1.079 1.08.5 1 2 2.16 Average wait in queue (min).1 4.16 Average wait in system (min).1.2 2 2.59 Average queue length.2.4 4.99 Average # of customers in system.