財(cái)務(wù)管理與財(cái)務(wù)分析運(yùn)營(yíng)管理課件c(編輯修改稿)
2024-09-28 16:19 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 ve… Mean = ?T Variance = ?T 169。 2020 Pearson Education ? The exponential distribution describes the probability that the service time will be no more than T time periods. Probability Distributions Service time If the customer service rate is three per hour, what is the probability that a customer requires less than 10 minutes of service? P(t ≤T) = 1 – e?T μ = average number of customers pleting service per period t = service time of the customer T = target service time P(t ≤ hr) = 1 – e3() = 1 – = Example Mean = 1/? Variance = (1/? )2 169。 2020 Pearson Education Operating Characteristics ? Line Length: Number of customers in line. ? Number of Customers in System: Includes customers in line and being serviced. ? Waiting Time in Line: Waiting for service to begin. ? Total Time in System: Elapsed time between entering the line and exiting the system. ? Service Facility Utilization: Reflects the percentage of time servers are busy. 169。 2020 Pearson Education SingleServer Model ? The simplest waiting line model involves a single server and a single line of customers. ? Assumptions: ? The customer population is infinite and patient. ? The customers arrive according to a Poisson distribution, with a mean arrival rate of ? ? ? The service distribution is exponential with a mean service rate of ?? ? The mean service rate exceeds the mean arrival rate. ? Customers are served on a firste, firstserved basis. ? The length of the waiting line is unlimited. 169。 2020 Pearson Education ? = Average utilization of the system = ? ? L = Average number of customers in the service system = ? ? – ? Lq = Average number of customers in the waiting line = ?L W = Average time spent in the system, including service = 1 ? – ? Wq = Average waiting time in line = ?W Rn = Probability that n customers are in the system = (1 – ?)?n SingleServer Model 169。 2020 Pearson Education SingleChannel, SinglePhase System Arrival rate (?? = 30/hour, Service rate (?? = 35/hour Average time in line = Wq = () = hour, or minutes Average time in system = W = = hour, or 12 minutes 1 35 – 30 Average number in line = Lq = (6) = customers Average number in system
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