D/D/1 Park Gate Simulator

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Park Gate Queuing Simulator (D/D/1 with Dynamic Arrivals)

Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 8:00 A.M., at which time vehicles begin to arrive at a rate of 480 veh/h. After 20 minutes, the arrival flow rate declines to 120 veh/h, and it continues at that level for the remainder of the day. If the time required to distribute the brochure is 15 seconds, and assuming D/D/1 queuing, describe the operational characteristics of the queue.

Simulation Controls

Server Parameters

Service Time ($T_s$) in Seconds:

Calculated Service Rate ($\mu$): 240 veh/h

Time-Dependent Arrival Rates (veh/h)

8:00 AM - 8:20 AM ($\lambda_1$): After 8:20 AM ($\lambda_2$): Total Simulation Time (Minutes): Animation Speed: 5x

Real-time Visualization

Current Time: 8:00 AM

Status: Ready

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IDLE Server 1

Key Metrics & Results

Current System State

Utilization ($\rho$): --

Current Queue Length ($L$): 0

Peak Metrics (So Far)

Max Queue Length ($L_{max}$): 0 vehicles

Max Waiting Time ($W_{max}$): 0 minutes

Queue Clears At: --

Summary & Graphs

Queue Length vs. Time (L vs. t)

Cumulative Flow (N-A Diagram)