Exponential distribution shows a statistical
Therefore, it is quite common for queuing system patients arriving during rush hour (early afternoon) wait their turn treatment by the doctor. Therefore, a proposal was made to assign a second doctor in multi queue develope the emergency room during peak hours, so they can respond to emergencies both at the same time. He asked the hospital administrator engineer to investigate this possibility. Administrator The engineer began to collect relevant data and historical data to predict the next year. He acknowledged that the ER is a queuing system and various models of the theory of queues characteristics predict the system used by two doctors. The engineer has concluded that emergencies happen almost at random (Poison entry process), so that the inter arrival times exponentially distributed with an average of one half hour is also found that the time required for the doctor treating patients approximately follows an exponential distribution.
A doctor requires an average of minutes the patient. Patients come. The engineer manager observed that patients not treated on a first come, first out. Instead, it seems that the nurse who performs the admissions divided patients into three categories: critical cases where immediate treatment is vital for survival; severe cases, where early treatment queuing system is important in order to prevent further damage and stable in case the treatment may be delayed without adverse medical consequences. Subsequently, the patients are treated in order of priority, where patients usually serve in the same category on a first in, first out. A physician treating a patient stopped when a new comes a higher priority class.
Some patients fall into the first category, the second and the third. As the most severe cases after receiving emergency treatment in hospital are hospitalized, the average processing time for a doctor in the emergency room is not much between these differences. The engineer decided to use the queuing model of the priorities of the discipline as a reasonable representation of the Friendly Skies Airline line system maintenance base has facilities for repair only an engine at a time. Therefore, the plane back in a service as early as possible was policy has been to substitute each plane the recovery of the four motors. In other words, a single motor repaired every time you walk into a hangar. With this policy, the planes arrive queuing system randomly at an average rate of one per day.
The time required for the repair of a motor (job once started) an exponential distribution with the average day. He made a proposal to change the policy so that the four engines repaired in succession each time an aircraft is in the hangar. This would mean that each aircraft would need the quarter maintenance basis to arrive in time. Since queuing system the time that is needed to fix an engine has theory that the time it takes to repair four engines has a distribution with a mean and four times a shape parameter. Now, management must decide queuing arrange to continue working as it did or to approve the proposal. The goal is the average flight time per day lost due to the entire fleet to minimize engine repairs.
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A queue can be divided into two main components, the tail and the service center. Arrivals are units which enter the system for the service. Once the service is completed, arrivals are converted into outputs. Both components of the system related costs that must be queuing system considered. Although the theory of queues provides important information not just a tool makes it possible situations’ kind of system require decisions arise in many areas, so it is impossible to make a general procedure applies to all situations tail optimal decision to present.