Vacation and priority - compulsory test
- Due 19 Feb 2024 by 10:00
- Points 1
- Submitting a file upload
1. Consider an M/G/1 queue with vacation. The arrival intensity is 0.5 arrivals per minute and average service time is 1 minute. Give the average remaining vacation time, given that the server is on vacation. Give the average remaining vacation time, considering both the busy and the vacation state of the server. Assume Exponentially distributed service times. Give the expected waiting time of an arbitrary request in the queuing system. Consider these two versions of the vacation time distribution:
a) The vacation times are Exponentially distributed with a mean of 1 minute.
b) The vacation time is always exactly 1 minute.
2. Consider a preemptive resume priority system as discussed in class. There are two priority classes with arrival intensities lambda_1, lambda_2, and service intensities mu_1 and mu_2. Which of these parameters affect the expected time low priority customers have from the first point of time they enter the server until they finally get served and leave the system? Give the intuitive explanation, why.