CSE412 - Assignment-2  - Multiple-server queueing system simulation - Solved

Simulation and modeling lab 



 

•       Consider an office building with 12 floors (numbered 1–12). There are four elevators (servers) which service the building. Each elevator has a maximum capacity of 12 passengers.  

 

•       People (customers) enter the lobby of the building at floor 1 and take an elevator to their destination floor (floor 2 to floor 12). Each customer selects the first available elevator (numbered 1–4). When a person enters an elevator and selects the floor of destination, the elevator waits 15 sec (door holding time) before closing its doors. If another person arrives within the 15-sec interval, the waiting cycle is repeated. If no person arrives within the 15-sec interval, the elevator departs to deliver all of its passengers. It is assumed that, even if fully loaded with 12 passengers, the elevator waits 15 sec before departing. We assume no other passengers are picked up along the way. After delivering its last passenger, the elevator returns to the main floor, picking up no passengers on the way down. When a person arrives in the lobby and no elevator is available (because all four elevators are transporting their load of passengers), a queue begins to form in the lobby.

 

•       We assume that it takes 5 sec for an elevator to travel between floors, 3 sec to open and 3 sec close its doors, and 3 sec for each passenger to disembark. We also assume that it takes 3 sec for each passenger in a queue to enter the next available elevator.

 

•       A customer chooses a floor with equal likelihood [uniform probability distribution U (2, 12)].

 

•       The interarrival times of customers are exponentially distributed with mean 1.50 minutes. Customers arrive in batches with the maximum batch size of 6.  We may generate this random variate in the following way. Consider 5 coins (fair coin) are tossed. The total number of heads, x, is binomially distributed between 0 to 5 [binomial (t, p) with t = 5, p = 0.5]. Next, 1 is added to this number x [a shift or change of location by +1]. Then we get a number y between 1 to 6 which is the random variate for batch size.

 

•       The simulation terminates when the simulation clock value exceeds 10000 sec.

 

•       For performance measure, we consider the following quantities:

1)      Total number of customers serviced during the entire simulation

2)      queue length means the number of customers in queue

3)      (delay time)i means the time customer i waits in a queue before stepping into an elevator

4)      (elevator time)i means the time customer i spends in an elevator

5)      (delivery time)i means the time required to deliver customer i to destination floor from time of arrival, including any waiting time.

6)      (load size)j means number of occupants of elevator j when it departs from floor 1

7)      (operation time)j means the total time elevator j operates (running between floors) during the entire simulation

8)      (available time)j means the total time elevator j spends in floor 1 being available for loading

9)      (number of max loads)j means the total number of times elevator j departs from floor 1 with full load of 12 customers during the entire simulation

10)  (number of stops)j means the total number of stops made by elevator j during the entire simulation

 

For quantities 2, 3, 4, and 5, you should keep track of both the average and the maximum. For quantity 6, you should keep track of the average. Quantity 1 is directly available from a counter variable. Quantity 2 can be calculated as a time-average similar to the way average number in queue was calculated in assignment-1.  Quantity 3, 4, and 5 can be calculated similar to the way average delay in queue was calculated in assignment-1.  The rest of the quantities can be obtained by keeping statistical counters. For example, for calculation of quantity 6, for each elevator, you may keep two statistical counters: One variable to keep track of how many times it departed from floor 1, and another variable to accumulate the total number of passengers it carries while it departs from floor 1.  

 

Format of the Input:

10000  // simulation termination  

12         4           12        6        // number of floors, elevators, capacity, batch size

15         5          3          3    //door holding time, inter-floor traveling time, opening time, closing time   

3          3       // passenger embarking and disembarking time

1.5      // mean interarrival time

 

Format of the Output: The output can be presented in a tabular format like the following table:

  

All times are measured in seconds and rounded to the nearest second.

You may present the result by having 10 simulation runs and taking averages of the quantities rounded to nearest integer. The above table was an example taken from a text book. You may present your obtained result by multiple tables (for example, one table showing elevator statistics, another one showing customer statistics).