Question

Consider the following queueing system of one server. Interarrival times are exponentially distributed with mean of 40 minute, there was little data available for processing times, but it was known that the minimum time is 35 minutes and maximum time is 65 minutes, but it is usually taking 40 minutes to process a job. a. Generate the needed random numbers from the set [0.43070, 0.22671, 0.00152, 0.81326, 0.89428, 0.16368, 0.57659, 0.79424, 0.57604] to simulate the interarrival times and processing times for a queueing system with one server. Round the results to the nearest integer.

Answer 1

To simulate the interarrival times and processing times for a queueing system with one server, you can use generated random numbers and formulas for exponential distribution and linear interpolation.

Step-by-step explanation:

To simulate the interarrival times and processing times for a queueing system with one server, we need to generate random numbers from the set [0.43070, 0.22671, 0.00152, 0.81326, 0.89428, 0.16368, 0.57659, 0.79424, 0.57604].

For the interarrival times, which are exponentially distributed with a mean of 40 minutes, we can use the formula:

Interarrival time = -40 * ln(random number)

Rounding the results to the nearest integer, we get the following interarrival times: [68, 89, 277, 20, 16, 100, 48, 22, 49].

For the processing times, we know that the minimum time is 35 minutes, the maximum time is 65 minutes, and it usually takes 40 minutes. We can use linear interpolation to generate the processing times based on the random numbers and the range of possible processing times. Rounding the results to the nearest integer, we get the following processing times: [42, 50, 35, 58, 61, 37, 46, 56, 46].