For example, in queueing theory, if we are comparing two different configurations of tellers in a bank, we would want the ( random ) time of arrival of the " N " th customer to be generated using the same draw from a random number stream for both configurations.
42.
Throughput is essentially synonymous to digital bandwidth consumption; it can be analyzed mathematically by applying the queueing theory, where the load in packets per time unit is denoted as the arrival rate ( ), and the throughput, in packets per time unit, is denoted as the departure rate ( ).
43.
Logistics engineers work with complex mathematical models that consider elements such as mean time between failures ( MTBF ), mean time to failure ( MTTF ), mean time to repair ( MTTR ), failure mode and effects analysis ( FMEA ), statistical distributions, queueing theory, and a host of other considerations.
44.
One version of the theorem, also known as "'Campbell's formula "', entails an integral equation for the aforementioned sum over a general point process, and not necessarily a Poisson point process . and queueing theory as well as the related fields stochastic geometry, and spatial statistics.
45.
This had led to convergence theorems of point process operations, which have their origins in the pioneering work of Conny Palm in 1940s and later Aleksandr Khinchin in the 1950s and 1960s who both studied point processes on the real line, in the context of studying the arrival of phone calls and queueing theory in general.
46.
Leonard Kleinrock conducted early research in queueing theory which proved important in packet switching, and published a book in the related field of digital message switching ( without the packets ) in 1961; he also later played a leading role in building and management of the world's first packet-switched network, the ARPANET.
47.
These point processes are frequently used as models for random events in time, such as the arrival of customers in a queue ( queueing theory ), of impulses in a neuron ( computational neuroscience ), particles in a Geiger counter, location of radio stations in a telecommunication network or of searches on the world-wide web.
48.
A 2002 article listing the most important contributions to operations research from 1954 to date listed four from Saaty : " Parametric Programming " ( 1954, with S . I . Gass ), " Mathematical Methods of Operations Research " ( 1959 ), " Elements of Queueing Theory " ( 1961 ), and " The Analytic Hierarchy Process " ( 1980 ).
49.
:: : ( Unsourced information follows ) I was told in the late 80s by a Operational Researcher I knew who claimed to be one of the national experts on queueing theory in Britain that the combined queue was significantly worse than individual queues both for overall throughput and for the counter staff, in both cases because of the accumulated dead time while the next customer notices that there is a position free and walks to it.
50.
Full-time faculty members include Clifford Stein who is an authority in Algorithms and former chair of the Industrial Engineering and Operations Research Department, Maria Chudnovsky, 2012 MacArthur Award recipient and one of the " Brilliant Ten " by Popular Science Magazine, Ward Whitt, an authority in Queueing Theory and Stochastic Process and committee chair of National Academy of Engineering, and the late Cyrus Derman, an authority in Operations Research who advised Sheldon M Ross, the author of many widely used textbooks for Statistics, Stochastic Processes, and Monte Carlo Simulation, for his PhD at Stanford.
