Queuing theory is a concept employed in solving demand for limited resources or services at a given time. It covers a wide range of field situations, for instance, computer management network, manufacturing scheduling, logistics and distribution. This article specifically explores the application of this theory in a logistics situation. EBDD company faces a hurdle in truck deliveries clogging the loading dock area. A little background information on the situation; the average arrivals of trucks per hour is 3.5 arrivals; the average time used in offloading a truck is 4.2 trucks in every hour; the system operates for 8 hours every day. The discussions of this report ( see attached excel file ) apply Little's theorem to determine the average number of trucks in the system. Basic model queuing and system state probability formulas are employed to determine the chances of having more than five, six or seven trucks in the loading dock area if we only have one unloading team (single server system). We also try to estimate the highest number of trucks with a 95% probability in the system. Then we consider the probabilities for five or fewer trucks in the system at any time given an additional unloading team (multiple service system).
We assume that the trucks generally arrive at the loading dock at random times, are served one at a time in the order they come (no truck receives priority), and the unloading team handles every truck. The single system implicitly assumes there is no upper limit on the system limit (at least none that can be specified) or on the population of trucks that may enter the queue. Furthermore, the queuing theory in this EBDD case scenario is that the inter-arrival time has an exponential probability distribution with a mean arrival rate of λ (lambda) truck arrivals and a mean service rate of µ(mu) offloaded trucks per unit time (every hour). There is no unusual truck or offload team behavior. Generally, the system uses First-in-First-out (FIFO) service discipline and that the average arrival rate is less than the average service rate, i.e., λ<µ
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