Question

An owner of a petrol pump with single attendant wishes to perform a simulation of operations to see whether any improvement is possible. He studied the system and found that an average of 6 customers arrive for service with random arrival times and form a queue, and the attendant provides a service exactly 9 minutes. For simulating the arrival times of customers, he has selected 10 random numbers with expected length of interval equal to one as

3.62 ; 1.78 ; 1.84 ; 1.31 ; 1.27
0.14 ; 1.71 ; 0.77 ; 0.97 ; 1.37
Find
(i) The total idle time for the attendant
(ii) Total waiting time for the customers, and
(iii) Maximum queue length during this period. If the service time is reduced to 6 minutes what is quality of service?

Answer 1

Without specific arrival and service initiation time data, it's not possible to calculate the exact total idle time, total waiting time, and maximum queue length. A reduction in service time should, in general, improve waiting times and queue lengths.

Step-by-step explanation:

Simulation of Petrol Pump Operations

The petrol pump scenario described involves an exponential distribution of customer arrival times and fixed service times. Given that on average, one customer arrives every two minutes, and the service time is exactly nine minutes, we can model this system to determine various metrics of interest such as total idle time, total waiting time, and maximum queue length. When the service time changes to six minutes, we can assess the improvement in the quality of service considering reduced waiting times and potentially shorter queues.

Calculating Total Idle Time and Other Metrics

However, to accurately calculate the (i) total idle time for the attendant, (ii) total waiting time for the customers, and (iii) maximum queue length, we would need additional information on the distribution of arrival times and customer service initiation times. Without such data, we can only establish that a shorter service time should lower the waiting time for customers and could reduce the queue length, thus enhancing the quality of service