Several Compound Poisson Distributions With Applications In The Probability Models Of Batched Customers Coming

Inventory management and queuing theory as a branch of operations research, with the requirements of economic development, its theory more seriously by most scholars, the theory has improved steadily, the paper is concerned with inventory management strategy and research at random queuing model theory. Based on the number of tourists (s,S) superimposed inventory policy and the single desk hordes queuing model under random conditions demand obedience random geometric Poisson distribution inventory management systems and queuing systems, introduced a discrete compound Poisson distribution family, as well as its two in this special case has important applications distribution:Hermite Poisson distribution and geometric distribution (also known as Polya-Aeppli distribution) the nature of the distribution. As geometric Poisson distribution to maximize profits, and inventory management application, analysis examples evenly distributed in obedience, Poisson distribution, Poisson distribution and geometric order to determine how to make the amount of the maximum average profit gained in profit maximization problem; Analysis in Inventory Management obey geometric Poisson distribution demand (s,S) inventory strategies (where s represents the lower bound of storage, S indicates the storage sector, when the weekend ordering inventory is less than s, so that early next week stock reaches S or not ordering). Obtained under the same conditions, the demand follows a geometric Poisson distributed demand obedience s, s value than the value of Poisson distribution to large. As geometric Poisson distribution in queuing theory application, for simplicity, we consider the-number of customers coming to obey source parameter (aλ,(1-a)λ) Hermite distribution (probability a customer service requirements once in 1-α probability distribution service requirements Hermite twice) service hours subject to parameters of single-server queuing model negative exponential distribution, given the phenomenon of a single jump the queue queuing service model in the steady state of the system and the probability of a customer’s system n the average number of customers and average waiting customer number and verify that the time when α = 1, at steady state, the system has a probability of n to pn=(1-p)p" customer. (Ie customer arrival is the Poisson parameter λ flow, service time parameter subject to a single-server queuing model (M/M/1 model) for the μ negative exponential distribution.) And the average number of customers in the system, at the same time draw jump the queue will increase customer wait, idle reduction Desk conclusion. Then consider the complex superposition of arrival (superposition of greater than 2) case, r tourists obey argument discrete complex Poisson (customer come up to r is a superposition of) a single service model in steady state methods the system calculates the probability that a customer’s n, queuing theory for this promotion process, also called generalized homogeneous birth and death process, if the customer’s arrival is subject to geometric Poisson distribution, we can also use a r discrete compound Poisson distribution parameters do approximation. This is the innovation of this paper.