A gas station only has one pump for refueling the Pertamax type. The arrival of Pertamax-fueled cars to the gas station follows the process Poisson with an arrival rate of 15 cars / hour. However, when this pump is being used (there is cars that are filling Pertamax), potential customers who come can move to another gas station. In particular, if there are n cars at the gas station, chances are potential customers who come, will move to another gas station is n / 3, for n = 1, 2, 3. The time needed to serve a car is exponentially distributed with an average of 4 minutes.

a. Draw the transition diagram and write the balance equations for the system this queue.

b. Complete equilibrium equations to obtain the proportion of time long term number of cars at the gas station.

c. Determine the expected waiting time of a car in this queue system.

  • $\begingroup$ Hello, @Yohanes Johan, welcome to MSE. Can you please add (in the question, not in a comment) what you have tried yourself and what you have found? That makes it easier for others to help. $\endgroup$ – Ernie060 Nov 7 '18 at 16:41
  • $\begingroup$ Maybe start by looking at standard results (b & c) for M/M/1 queue without restrictions on queue length. Then look at similar results for M/M/1/4 queue where there can be at most 4 cars in the system. Your answer should be btw thes two. // Notice that departure and attempted arrival rates are the same. $\endgroup$ – BruceET Nov 8 '18 at 2:27

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