Waiting Lines-Queuing Theory 1. Duri ng tax season the H&R; BLOCK hires seasonal

Question

Waiting Lines-Queuing Theory 1. Duri ng tax season the H&R; BLOCK hires seasonal Tax Accountants to help answer the questions of taxpayers who call at the office for elp. Suppose that customers arrive at the office at an average rate of 60 per hour and follow a Poisson distribution. An accountant can handle an average of 5 customers per hour with service times, exponentially distributes. Assume that there are 10 accountants and when they are all busy, the there are 5 additional seats in the waiting room. Excess customers are advised to come back later if the waiting room is full. H&R; BLOCK QUEUE 1: M/M/C/K STATISTICS(time units QUEUE hrs) Mean arrival rate. Mean service rate per server 10 60.0000 5.0000 . .. .. 95.6087 Mean server utilization (%) … … … Expected number of customers in queue....2.4506 Expected number of customers in system... 12.0114 Probability that a customer must wait.... 0.8111 0.2033

Explanation / Answer

a. When an accountant worker is busy, customer will be waiting. Probability that a customer must wait is 0.8111. Therefore, an accountant worker is busy 81.11% times.

b. Expected numbers of customers in the system is 12.0114.

c. Average number of callers waiting for a turn to talk to the IRS workers is the expected numbers of customers in the queue, i.e., 2.4506.

d. Probability that a customer must wait is 0.8111.

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