A fast food restaurant has a drive-through window with a single server. Customer

Question

A fast food restaurant has a drive-through window with a single server. Customers arrive at the rate of 15 per hour and the servive time is 3 minute per customer. Determine the. A) customer average waiting time in line (do not include the customer being served) B) average number of customers in line including the person being served C) probability that 2 customers are in line including the person being served. D)probability that the server is idle e) Do you recommend to add one more server? Explain your reason.

A queing model is needed from excel.

Explanation / Answer

= 15 per hour µ = 20 per hour (3 per minute) Average Utilization of the system p = / µ = 15/20 = 0.75 Probability that there are 0 customers in the system P0 = 1 - p = 1 - 0.75 = 0.25 Average number of customers in waiting line = Lq = pL = / µ * / µ - = 15/20 * 15 / (20 - 15) = 0.75 * 3 = 2.25 customers Average number of customers in line including the person being served = L = / µ - = 15 / 20 - 15 = 3 customers Probability that 2 customers are in line including the person being served P2 = (1-p) * p^2 = 0.25 * 0.75^2 = 0.140625 Probability that the server is idle = 1 - p = 1 - 0.75 = 0.25 = 15 per hour µ = 20 per hour (3 per minute) s = 2 Average Utilization of the system p = / Sµ = 15/(2*20) = 0.375 Probability that there are 0 orders in the system (P0 = 1 / [1 + / µ + {( / µ)^s / s!} * (1 / 1-p)] = 1 / [ 1 + 15/20 + (15/20^2 / 2!) * (1 / 1 - 0.375) ] = 1 / [ 1 + 0.75 + 0.45) = 1 / 2.2 = 0.4545 Average number of customers in waiting line = Lq = P0*(/µ)^s*p / s! (1 -p)^2 = (0.4545 * 15/20^2 * 0.375) / (2! * 0.625 ^2) = 0.095881 / 0.78125 = 0.122727 customers Yes - it is worth introducing second automatic machine as service levels increase drastically from 2.25 customers in line to 0.1227 customers

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