Uniform fractional part: a simple fast method for generating continuous random variates

A known theorem in probability is adopted and through a probabilistic approach, it is generalized to develop a method for generating random deviates from the distribution of any continuous random variable. This method, which may be considered as an approximate version of the Inverse Transform algorithm, takes two random numbers to generate a random deviate, while maintaining all the other advantages of the Inverse Transform method, such as the possibility of generating ordered as well as correlated deviates and being applicable to all density functions, regardless of their parameter value

Service Rate Control in Mn/Gn/1 Queue

Part 5: Smart Production for Mass CustomizationInternational audienceService rate control in queues is an important problem in practice. For example, when the number of customers waiting for finished products is small production has a normal speed, but if it is greater, the production speed should be faster to meet the demand. For an exponential service time distribution, the optimality of the threshold type policy has been proved in literature. On the other hand, in production systems, production time follows a general distribution in general. In this paper, service control of speed depending on the number of customers is discussed. The analytical results of an M/G/1 queue with arrival and service rates depending on the number of customers in the system, which is called an Mn/Gn/1 queue, are utilized for computing performance measure of service rate control. Constant, uniform and exponential distributions on the service time are considered through numerical experiments. The results show that the optimal threshold depends on the type of the distributions even when the mean of service time is the same