+1 (845) 317-8489 [email protected]
Select Page

Consider the following Emergency Operation situation:
A city has just experienced a minor earthquake, and many of its citizens have been injured. An emergency relief center has been set up to tend to the apparent large number of wounded citizens.
Due to the physical limitations of the relief center, two stations (A and B) have been set up in series. Incoming citizens must first proceed to Station A, a triage station in which the attending physician examines the individual and determines the extent of the injury; once the extent has been determined, the individual then proceeds to Station B for treatment.
The following arrival and service processes for station A are as follows:
Station A:
Inter-arrival times are exponential, with a mean of 5 minutes.
Processing times (i.e., examination) is uniformly distributed over the range of 6 to 10 minutes.
Arrivals at Station B are the patients leaving from Station A.
Processing times (i.e., examination) is uniformly distributed over the range of 10 to 20 minutes. (Use random number STREAM 3 below).
Recall from Problem 1.27: For the exponential distribution with mean , compute the cumulative distribution function F(t); let RN be a random number drawn between 0 and 1; solve RN = F(t) for t; we saw that t = ln(RN). For example, take the first RN on STREAM 1 of the random number list at the end of this problem: RN = 0.305445. The calculated inter-arrival time then is (- 5) ln(0.305445) = 5.9 minutes; lets round to the nearest tenth.
You have to repeat what you did above but for the uniform distribution: if we have a distribution that is uniform between 6 and 10, in order for it to be a valid probability distribution, the area under its curve must be one. The uniform distribution is just a horizontal line extending between 6 and 10, and the area under it (which is a rectangle) must be 1. So the height of this rectangle must be 0.25 (0.25 times (10 6) = 1). So the uniform distribution function is f(t) = 0.25 for 6 t 10. Now compute F(t) which is the definite integral of f(t) between those 2 limits. (This is trivial!!), Then as above, let RN be a random number drawn between 0 and 1 (Use STREAM 2); solve RN = F(t) for t, and this is the examination time.
The following arrival and service processes for station B are as follows: