Assignment 8

Topic: Waiting line

The motor vehicles registration authority (Punjab Government) is reviewing its waiting lines management strategy at its main office in Lahore. Currently the offices use single-server single channel single-phase system. When processing token taxes and registration renewal. Based on historical evidence, on the average 9 customer arrive per hour. Arrival is described by a passion distribution. Staff serve at a rate of 12 customer per hour (with an exponential distribution). The customers coming from infinite population, do not show balking or reneging behaviour. The administration would like you to calculate the operational characteristic of the waiting line systems and decide in the following:

If the utilization of the system is below 70% they will nor hire more staff for any future expansion. If the utilization is between 70% to 80% , they will propose hiring of at 1 to 2 staffers in next quarter. If the utilization is higher than 80%, the office needs immediate new hiring.

1. Needed recommendation?
2. Average number of customers within the waiting line?
3. What is the probability of having more than 2 customer in the system at a given time?

Higher management believes that its time to introduce citizen- friendly governance in public services. Therefor it has to be decided if an average customer spends more than half an hour in the system, air conditioners, multiple TV screens and cold water dispensers in the customer area will have to be installed. If customers spend less than 10 minutes in the system only air conditioner will be required.

4. Decide

Staff will be assigned additional tasks assuming there is probability higher than 30% of having no customer at given time. With the given data, is this assumption correct or false?