Assignment Task:

Task:

1. Compile your answers to Problem 1, Problem 2 in a report, and submit it as a softcopy to the module’s Moodle website. Your report must be typed and the font size used must be 11 or greater. 

2. Submit the SIMUL8 file from Problem 2,part b) in *.S8 format on the module‘s Moodle website.

Please use your student ID number as your report and *.S8 file name (e.g. 351363.S8).

Do not mention your name anywhere in your submissions.

This is an individual assignment. Plagiarism or copying is not permitted and any offence will be dealt with under the University procedures. 

Throughout this assignment please use the following constants:

u = The first two digits of your student ID number v = The third and fourth digits of your student ID number w = The final two digits of your student ID number

             (e.g. A student ID number 351363 gives u = 35, v = 13, w = 63) 

Problem 1

Orders are received for one of four types of parts.  The interarrival time between orders is exponentially distributed with a mean of 10 minutes.  The table below shows the proportion of the parts by type and the time needed to fill each type of order by the single clerk.

(For example, 40% of orders are for type A parts, and the service time by the clerk for an order of type A part is normally distributed with mean 6.1 and standard deviation 1.1.)

Orders of types A and B are picked immediately after they are filled, but orders of types C and D must wait with waiting time uniformly distributed between 5 minutes to 15 minutes.  

Using SIMUL8, simulate 50 independent runs, of 8 hours in each run, to determine the proportion of orders that take less than or equal to 25 minutes through the process. Describe as clearly as possible in 300 to 500 words how your SIMUL8 model is built and also how you obtain the answer to the question asked.  Screenshots and computer outputs should be provided in your report. In particular, a screenshot of your model is to be provided. You do not need to submit the SIMUL8 file used to solve the problem. 

Use the number 1 as your initial random seed. 

[25 marks]

Problem 2

The student-center cafeteria at the University of Portsmouth is trying to improve its service during the lunch rush hour from 11:30am to 1:00pm.  Customers arrive together in groups of size 2, 3, 4 and 5, with respective probabilities 0.5, 0.3, 0.1 and 0.1.  Interarrival times between groups are exponentially distributed with mean 25 seconds.  Initially, the system is empty and idle, and is to run for the 90-minute period.  Each arriving customer takes one of three routes through the cafeteria (groups in general split up after they arrive):

• Hot-food service, then drinks, then cashier.
• Specialty-sandwich bar, then drinks, then cashier.
• Drinks (only), then cashier.

The probabilities of these routes are respectively 0.70, 0.20 and 0.10;  see figure below.  However, if there are more than 10 customers waiting in the queue at the hotfood counter or the specialty-sandwich bar which a customer intends to go to, then the customer will balk.  At the hot-food counter and the specialty-sandwich bar, customers are served one at a time.  The drinks stand is self-service, and we assume that nobody ever has to queue up here;  this is equivalent to thinking of the drinks stand as having infinitely many servers.  There are two cashiers, each having their own queue, and there is no jockeying; customers arriving to the cashiers simply choose the shortest queue.  All queues in the model are FIFO.

In the figure below, ST stands for service time at a station, and ACT stands for the accumulated (future) cashier time due to having visited a station;  the notation ~ U(a,b) means that the corresponding quantity is distributed uniformly between a and b seconds.  For example, a route 1 customer goes first to the hot-food station, joins the queue there if necessary, receives service there that is uniformly distributed between 50 and 120 seconds, “stores away” part of a (future) cashier time that is uniformly distributed between 20 seconds and 40 seconds, then spends an amount of time uniformly distributed between 5 seconds and 20 seconds getting a drink, and accumulates an additional amount of (future) cashier time distributed uniformly between 5 seconds and 10 seconds.  Thus, his service requirement at a cashier will be the sum of the U(20,40) and U(5,10) random variates he “picked up” at the hot-food and drinks stations.

Currently, there is only one employee at the hot-food counter and only one employee at the specialty-sandwich bar. 

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