# The arrivals of events with the constant rate are

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Unformatted text preview: ver, in stochastic models a probability distribution is associated with the arrival of events and the service times. In traffic and in most queueing situations the entities arrive to the system with a probabilistic inter-arrival time (IAT) distribution and the service times (ST) also have a probabilistic distribution varying for each entity. Furthermore the output variables of the queueing systems, length of the queue and the delay time for the entities are also probabilistic measures. The behavior of queues, number of entities waiting in the queue, and delay times cannot be solved with a straight forward mathematical approach unless IAT and ST are very well behaved mathematical distributions (e.g. Negative Exponential, Erlang, or Hyper-Poisson). Monte Carlo Simulation, run for many thousand times, can provide reliable answers, which are very specific and unique, for determining system countermeasures. Other methods, like deterministic simulations whe re arrivals and service times occur at periodic time intervals cannot accurately capture the behavior of such queueing systems. 3 1.1 Statement of the Problem Construction work zones on heavily traveled highways can cause problems for the motorists. Construction work zones may cause travel time delays, bottlenecks, and even accidents. Slowing and merging traffic is the main cause of the problems in construction work zones. Better planning of construction work zones before the starting of construction projects would decrease the problems associated with the work zone. In most of the construction work zones with high hourly traffic volumes, paved shoulders or medians are used to avoid the reduction of lanes. If the queue lengths and the delay times for the traffic in the construction work zone would be known in advance, then, the decision of whether or not a paved shoulder or median should be utilized for the traffic could be made with more accuracy. If no excessive queues and waiting times would be forecasted the cost of providing the extra temporary paved lanes could be avoided and a large amount of costs could be saved. A simulation approach could forecast the lengths of queues and the extent of delay times and alternative construction work zone solutions could be explored without affecting the motoring public. Simulation has the potential to help identify the outcomes of various configurations for construction work zone projects without actually affecting the motoring public. 1.2 Objective of the Study The objective of this study is to develop a traffic simulation model using ARENA simulation program to estimate the expected delays and queues using a probabilistic inter-arrival time distribution in construction zones and to investigate the capabilities and 4 limitations of the ARENA simulation program for modeling traffic when the number of lanes are reduced. Another objective is to use a procedure to measure the traffic in a real world situation and to process the time stamped traffic data in such a way that inter-arrival time distributions can be used in the ARENA simulation model. Furthermore, we also want to compare the results of the ARENA traffic simulation model with the QuickZone Delay Estimation Program, which uses a deterministic queueing modeling approach. 1.3 Scope of Work The first step of this study is to find out the available construction work zone simulation programs available in the public domain and literature and find out what the advantages and disadvantages of these simulation programs are. The second step of this study is to conduct a literature review to find out traffic behavior through the construction work zones. The third step of this study is to develop a simulation model for the construction work zone using the ARENA 7.01 simulation program by Rockwell Software. The fourth step is to analyze measured traffic in a real world environment and obtain probabilistic inter-arrival time distributions for different traffic volumes during a day in order to validate the simulation program. The fifth step is to compare the ARENA simulation program output with the QuickZone delay estimation program output. 5 2 2.1 LITERATURE REVIEW Work Zone Simulation Programs Evaluation Studies QuickZone work zone delay estimation program, which was developed by The Federal Highway Administration (FHWA) in cooperation with Mitretek Systems [4], uses a deterministic inter-arrival time distribution for the estimation of the output parameters. It uses a deterministic queueing model to simulate traffic going through work zones to determine when there would be traffic backups. It is a tool intended for highway engineers to determine how to set up a work zone to minimize traffic disruption. QuickZone provides four primary outputs—a delay graph, a travel beha vior summary, an amortized delay and construction cost graph, and a summary table. Detailed description of the QuickZone delay estimation program is given in section 3.3. In a study by Maze and Kamyab [2], a work zone simulation model was d...
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