Section 1: Queuing Theory

Question 1:

Travelers arrive at an airline smart check-in with a mean rate of 50 travelers per hour. Based on the FCFS service discipline, a traveler is served every 1 minute on average and leaves the check-in. We assume that the airline smart check-in queueing system is an M/M/1 process is steady-state condition.

Calculate L; the expected number of travelers in the airline smart check in queuing system. Explain your answer

Question 2:

What is the distribution type of the interarrival times of M/M/1?

Question 3:

Trucks enter a queue on FCFS basis. The arrivals follow a Poisson distribution, while service time follows an exponential distribution. If the arrival rate is 18 per hour and the service rate of a single-server is 20 per hour, what is the average length of the queue approximately Lq? Explain your answer

Question 4:

The average arrival rate of 2 customers per hour to a single server, single phase queuing model is the same as (on average), what is the average time between arrivals?