# Waiting Line Case: Polonius National Bank

Essay by doudouUniversity, Master's May 2006

The Case.

The goal of this case study was to gain a further understanding and application skills of waiting line analysis. This case analyzed the existing staffing policies for Polonius National Bank (PNB). The goal of the analysis was to determine the optimal number of cashiers that the bank should staff using a waiting line model. Once this optimal number of cashiers was decided upon, it was necessary to determine for what range of goodwill costs the number of cashiers would remain the same.

Data.

The data was gathered at a particular time when the arrival rates and service time patterns were expected to be consistent on a day to day basis. It was determined that this time was from 9:00 A.M. to 11:30 A.M. A branch employee recorded the number of arrivals during randomly chosen minutes on several different days, during the selected time window. Table 1.1 in the appendix shows the data recorded.

Also recorded by the employee was the service time each customer required to complete their transaction. The time did not include the amount of time the customers spent waiting in line. This data can be found in Table 1.2 in the appendix.

Distribution Computations.

With all the appropriate data acquired, an analysis was conducted. The first step in the analysis was to determine the expected arrival rate (ÃÂ»). This was determined by first finding the total number of time segments observed, found to be 1273. The probability of arrivals per minute was determined by dividing the number of occurrences for each arrival rate per minute, ranging from 0 customers per minute to 18 customers per minute, by the total number of observed minutes. The product of the arrivals per minute and the probability was calculated for each number of arrivals. This was then summed to...