Question

You have been asked to analyze the queue for registrations for a popular MSOM seminar at a major national conference. Conference attendees arrive to register at the rate of 5 people every 15 minutes (Poisson distributed). It takes each host, any number of which can be hired directly through the conference at the cost of $17 per hour, 7 minutes to register a guest, following a negative exponential distribution. The conference recognizes a waiting cost of $40 per hour per guest in line. A single waiting line is set up, but can accommodate multiple servers. What is the minimum number of hosts that could be hired for this system?

Answer 1

Step-by-step explanation:

Average arrival rate, λ = 5 people in 15 minutes = 20 people in 60 minutes = 20 per hour

Average service rate, μ = 1 in 7 minutes = (60/7) per hour

The minimum number of servers required for a stable queuing system = λ / μ = 20 / (60/7) = 7/3 = 2.333

So, the minimum number of hosts that could be hired = 3 hosts