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# Other Examples

Example 3.1: Able and Baker, revisited.

• System state:
• : the number of cars waiting to be served at time t.
• : a boolean variable indicating Able being idle or busy at the time.
• : a boolean variable indicating Baker being idle or busy at the time.

• Entities: cars and the two servers.

• Events:
• arrival event
• service complete by Able event.
• service complete by Baker event.

• Activities:
• interarrival time
• Able's service time
• Baker's service time

• Delay: a customer's wait in the queue until Able or Baker is free.

Example 3.3: Single-channel queue (Supermarket check-out counter).

In conducting an event-scheduling simulation, a simulation table is used to record the successive system snap-shots as time advances.

The simulation table is Table 3.1 on page 72.

System state:
(LQ(t), LS(t)) where LQ(t) is the number of customers in waiting line, and LS(t) is the number of customers in service at time t.

Entities:
Server and customers.

Events:

• Arrival (A)
• Departure (D)
• Stopping event (E), scheduled to occur at time 60.

Event notices:

• (A,t) representing an arrival event to occur at future time t.
• (D,t) representing a departure event to occur at future time t.
• (E,60) representing the stopping event to occur at future time 60.

Activities:

• Interarrival time, defined in Table 2.6 page 28.
• Service time, defined in Table 2.7 page 28.

Example 3.4: The check-out counter simulation, continued.

Further from Example 3.3, we want to collect some statistics, mean response time and mean proportion of customers who spend 4 or more minutes in the system (time in the system includes waiting time and service time).

• mean response time =
• mean proportion of the customers who spend 4 or or minutes =

Example 3.5: The dump truck problem.

• Six dump trucks haul coal from the entrance of small mine to the railroad.

• After loading, a truck moves immediately to the scale to be weighed as soon as the scale is available.

• The two loaders and the scal have a first-come-first-server queue.

• Aftger being weighed, the truck drives off and will come back to the same line, to get smore coal. This process is repeated.

The model has following components.

• System state: [LQ(t), L(t), WQ(t), W(t)]
• LQ(t) = number of trucks in loader queue
• L(t) = number of trucks in loader (0, 1, 2)
• WQ(t) = number of trucks in scale's waiting queue.
• W(t) = number of trucks being weighed (0, 1, or ).

• Event notices
• (ALQ, t, DTi) dump truck i arrives at loader queue