A batch arrival queue providing a class of truncated geometric distribution for modeling distribution of animal populations

摘要

We consider a batch arrival queueing system M ^{( i )}/ M /1/ m / of varying cluster arrival sizes I. The arrival process thus constitutes an independent compound Poisson stream of rate l _r where and pr ( I ? i ) = b _i with b _k =0 for k ? 0. Acceptance into system is further limited by available space m thus implying a truncation of an otherwise infinite domain. With the aid of certain combinatoric analysis of partitions and compositions the steady state distributions under various forms of arrival size pattern have been explicitly obtained in terms of system specifications. It is demonstrated that the results can perfectly provide one more class of truncated geometric distribution for a less idealistic modeling of the complex natural process of aggregation, congregation and abundance for such animals as soil microarthropods. A numerical illustration is provided using some copious data from the biological literature.