However, these display features are purely for visualization purposes the positions of the servers and customers, and the colors of the customers, have no functional purpose or impact. This model displays servers in a row along the bottom of the NetLogo world customers are shown in a queue which "snakes" from near the bottom of the NetLogo world to the top. In this model, these unbounded values are denoted by "N/A" in the associated monitors. If the theoretical server utilization - determined by multiplying the arrival rate by the service time, dividing by the number of servers, and taking the lesser the result of the calculation and 1 - is less than 1, then the queueing equations have a defined solution otherwise, the expected queue length and expected time in the queue are unbounded. In this model, these theoretical values are shown in the bottom row of monitors. When there is a single server, or when all the servers have the same mean service time, the steady state characteristics (if the system is capable of reaching a steady state) can be determined analytically. Poisson arrivals, exponential service times, infinite queue capacity and source population, FIFO queue discipline. In queueing theory notation, the type of system being simulated in this model is referred to as M/M/n - i.e. When any of the servers are busy, the scheduled time of service completion is shown in the label below the server. THINGS TO NOTICEĪfter the simulation has started, the next scheduled arrival time is always shown in the Next Arrival Time monitor. The aggregate statistics can be reset at any time - without emptying the queue or placing servers in the idle state - with the Reset Stats button. The simulation can be run one step at a time with the Next button, or by repeatedly processing events with the Go button. The latter allows for minimizing the effects of system startup on the aggregate statistics. The max-run-time and stats-reset-time control the length of the simulation and the time at which all the aggregate statistics are reset, respectively. These values can be changed before starting the simulation, or at anytime during the simulation run any changes are reflected immediately in a running model. The mean-arrival-rate and mean-service-time sliders control the arrival and service processes, respectively. Use the number-of-servers slider to set the number of servers then press the Setup button to create the servers and reset the simulation clock. Since these are the only events that can result in a change of the state of the simulation, there is no point in advancing the clock in smaller time steps than the intervals between the events. In this model, the different events are: customer arrival and entry into the queue (followed, if possible, by start of service) service completion, with the customer leaving the system (followed, if possible, by start of service for a new customer) statistics reset and simulation end. At each step, the clock is advanced to the next scheduled event in an event queue, and that event is processed. This is a discrete-event simulation, which is a type of simulation that advances the clock in discrete, often irregularly sized steps, rather than by very small, regular time slices (which are generally used to produce quasi-continuous simulation). Arrivals follow a Poisson process, and service times are exponentially distributed. It has a single, unlimited queue and 1-10 homogeneous servers. This is an extenstion of Nick Bennett's DEV queueing system model ( ). Do you have questions or comments about this model?
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