Assignment #3 Queue Analysis of the Tim Horton’s Lineup for Coffee solved




As mentioned in class, there are usually two ways in which customers are lined up for access to a
number of service windows. Typically in a bank, there is one queue line for everyone and a number of
windows. When a window becomes free, the next person at the head of the queue leaves the queue
and proceeds to the window. People coming into the bank simply join the single queue at the tail of the
At Tim’s in Geology, we have the other approach to providing service. Every service window has its own
queue. Typically when a person comes up to the lines, they choose the shortest line to join and then
stay in that line. It can frustrate some people to see the longer line actually move faster and sometimes
people will line hop (i.e. when the other line is shorter than the queue in front of me).
So which is the best approach? In this assignment we are going to try and determine that. Here are the
parameters for the simulation.
For both simulations you are to do the following:
 Run the simulation for 6 hours
 A new customer group arrives every 1 minute ± 58 seconds (i.e. as little as 2 seconds apart and
as much as 1 min 50 seconds apart
 A group will consist of 1 to 6 customers following this distribution:
o 1 person – 30%
o 2 people – 40%
o 3 people – 20%
o 4 people – 5%
o 5 people – 3%
o 6 people – 2%
Each person in the group joins the queue single file but we can use the same join time for each
member of the group.
 Average serving time for a customer is 2 minutes ± 65 seconds.
For each simulation below, report on the following:
 Maximum number of customers served
 Average number of customers served per window per hour
 Average wait time in the queue for each customer
 Maximum wait time in the queue
 Average queue length for each queue
 Maximum queue length for each queue
Simulation #1
Simulate a scenario with two server windows and two queues. When a group of customers arrive each
individual in the group will choose the same queue, but the first individual will choose the shortest
Simulation #2
Simulate a scenario with two server windows and one queue. Report on the same statistics as scenario
Based on your results of these two simulations, which queue configuration is the best, or is there no
Considerations for designing your simulation:
 You can use an ordered linked list for the event chain rather than actually running a clock
o List is ordered by increasing clock time
o Each list element has the event type (customer arrives and joins queue, customer leaves
queue and is at server window, customer leaves window), the clock time when the
event is to occur
 Use a queue for each lineup. The info at each element in the queue is a customer. Along with
the customer you need to record things like time when they joined the queue, time when they
approached the server window, amount of time in the queue, amount of time at the server
window. Then before destroying the customer object, update your statistics counts and totals
for final analysis
Consider the following UML to begin your development. It may be incomplete. Document fully any
changes or additions you may make to this design:
+SetTimeJOinQ() +SetTimeToWindow() +TimeInQ() : int +TimeAtWindow()
-timeJoinedqueue : int -TimeToWindow : int -CustomerNumber : int Customer +JoinQ() +LeaveQ() : Customer -MaxLength : int -TotalCustomers : int CustomerQ * 1
-info : Customer LinkedList4Q
1 +isEmpty() : bool +InsertInfo() +DeleteInfo() : -nextList : Llist -info -empty : bool
-Info : Event EventQueue +GenerateNextEvent() : Event -EventType -EventClockTime
Event 1 1 Note: The linked list that supports the CustomerQ must behave as a queue. The linked list that is the
EventQueue must be in order of event time, i.e. as you work from the rear to the front of the queue the
event time gets smaller. Consider:
Rear of event queue Front of event queue
When you generate the next event of the type pulled off the event queue front and it should occur at
11:35 it must be inserted between the event at 11:30 and the event at 11:49.
Submit all source code files and your data results which include the simulation raw data and the
calculated results in a Word doc or pdf.
This assignment is to be accomplished using extreme programming – pair up with someone in the class
and using pilot/copilot share the programming/overseeing duties as we discussed in class. It works best
if you share the duties even if one of you is a much more adept programmer.
Marking scheme:
50 marks – correct implementation of the classes and execution of the code.
30 marks – results and documentation.