Arrival Process Distribution Research Articles

Introduction to “Little's Law as Viewed on Its 50th Anniversary”

In 1961, Operations Research published a short, fivepage article by John D. C. Little, then of Case Institute of Technology (now Case Western Reserve University), entitled a “A Proof for the Queuing Formula: L= ‹W ” Little (1961). This paper has become one of the five most cited papers ever published in the journal. And its influence goes far beyond the professional literature. In the paper, Little proves that under very general conditions, the average length of a queue, in steady state, will be equal to the arrival rate into the queue times the average wait in the queue. Remarkably, this relationship is not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else. Nor does it depend on the structure of the queueing system: “Little’s Law” holds not just at the individual queue level but also at the system level. Complicated systems can be analyzed simply by looking at the queue length and waiting time relative to the system. For such a simple relationship, Little’s Law has had a tremendous impact in practically every field of endeavor. Whether you are trying to access a Web page of a heavily utilized server or standing in line at an amusement park attraction, Little’s Law governs the length of the wait for service. Little’s Law has been used to calculate the spread of genes in a population and in analyzing complex project management systems. Given the generality of the conditions that are needed for Little’s Law to apply, it acts as a quick heuristic analysis for systems of all kinds. Fifty years after publication, John Little has put together a paper (Little 2011) summarizing the influence of his original paper. In the new paper, he outlines both the theoretical advances and the practical applications of the Law. For a five-page paper with a forbidding title, the 1961 paper has had a tremendous impact on the profession and beyond. We are pleased to have this retrospective on this important anniversary. To celebrate this occasion, the OR Forum area of the journal has asked a number of luminaries to provide comments on the impact that the paper has had both on practice and on theory. These authors include Ron Wolff, Ed Kaplan, Tim Lowe, and Sridhar Tayur. Their comments are published in an online companion at http://orforum.blog.informs.org. This is also the place for readers of the journal and the community at large to share their experiences and comment on this beautiful piece of work published exactly 50 years ago!

Neural modelling and performance analysis of the link occupancy distribution for wireless broadband transmissions

This paper is devoted to neural modelling and performance analysis of the link occupancy distribution for wireless broadband transmission. Multiclass models of a single link transmission for rigid, adaptive and elastic traffic are developed, based on Markov rewards models. The link occupancy distribution is introduced as embedded, discrete time Markov chains researched with the use of Vector Quantification (VQ). Link occupancy performance is simulated as a combination of single queues with random distributions of arrival processes and holding time service phases. The density of occupancy probability is determined using Learning Vector Quantification (LVQ) in a two-layered neural structure.