Other Examples

Example 3.1: Able and Baker, revisited.

• System state:
  • $L_Q (t)$: the number of cars waiting to be served at time t.
  • $L_A (t)$: a boolean variable indicating Able being idle or busy at the time.
  • $L_B (t)$: 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 = $\frac{\sum_{i=0}^{i=n} depart_i - arrive_i} {n}$
• mean proportion of the customers who spend 4 or or minutes = $\frac{number~of~cusotmers~who~waits~4~ minutes~or~more} {total~number~of~customers}$

Example 3.5: The dump truck problem.

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

• Each truck is loaded by one of the two loaders.

• 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.

• The actual time for loading and weighing is negligible.

• 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
  • (EL, t, DTi) dump truck i end ends loading at $EL$ being loaded.
  • (EW, t, DTi) dump truck i ends weighing at time t.
• Entities: The six dump trucks (DT1, DT2, ..., DT6)
• Lists: loader queue and scale queue, both first-in-first-out.
• Activites: Loading time, weighing time, and travel time.
• Delay: Delay at loader queue, and the scale.

See Table 3.6 on page 77 for an illustration.