Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes

Operations Research at Bell Laboratories through the 1970s: Part II

“…In the 1960s and 1970s Segal, John W. Suurballe, and others developed optimization techniques for problems such as the design of private-line networks under various special rate structures for circuit usage and call miles, the analysis of bidding strategies for aluminum and other resources used in manufacturing cables, the design of hierarchical telecommunications networks with alternate routing (Segal 1964), the spacing of repeaters in the layout of transmission systems, and the conÿguration of integrated circuit chips to reduce crossovers. In another e ort, Shlomo Halÿn, McCallum, and Segal developed models for analyzing the growth of jumper congestion in central o ce main distribution frames (Halÿn et al 1972). Later, Halÿn worked on techniques for the optimal design of electronic ÿlters to meet speciÿc characteristics (Halÿn 1970a(Halÿn , 1970b and on queuing models for the ow of calls in switching systems and measures of customer service in a business o ce (Halÿn 1975a).…”

“…In another e ort, Shlomo Halÿn, McCallum, and Segal developed models for analyzing the growth of jumper congestion in central o ce main distribution frames (Halÿn et al 1972). Later, Halÿn worked on techniques for the optimal design of electronic ÿlters to meet speciÿc characteristics (Halÿn 1970a(Halÿn , 1970b and on queuing models for the ow of calls in switching systems and measures of customer service in a business o ce (Halÿn 1975a). Another important example of systems engineering work was that of Rath and his colleagues, who developed approximation techniques for analyzing the complex queuing characteristics of automatic call distributors with multiple queues and intraqueue over ows (Rath and Sheng 1979 Encouraged by earlier successes in the exchange network area, Bell Labs scientists also developed computerized capacity expansion and network analysis tools to study other aspects of the Bell System telecommunications network.…”

“…These developments included computer codes for nonlinear optimization by Richard W. Cottle and Saigal, as well as network analysis codes for constrained network ows and routing by Chen and Saigal, and by Burman, McCallum, and Suurballe. Other research on graph theory by Frank T. Boesch, Thomas, and others, on linear programming by Suurballe, and on integer programming by Halÿn was used in formulating and understanding the basic network and combinatorial optimization structure of many operational problems (Boesch and Felzer 1972, Thomas 1976, Marshall and Suurballe 1969, and Halÿn 1972a.…”

“…Finally, research in stochastic processes by Halÿn, Heyman, Segal, and others provided basic insights into improved methods for analyzing and characterizing operational problems in inventory management and queuing systems (Halÿn 1975b;Heyman 1974Heyman , 1975Heyman and Segal 1974;Segal 1970aSegal , 1970b. This fundamental work led to the development of basic methods for modeling and approximating complex stochastic systems made possible by the use of modern concepts in computer technology (Avi-Itzhak and Heyman 1973).…”

“…This fundamental work led to the development of basic methods for modeling and approximating complex stochastic systems made possible by the use of modern concepts in computer technology (Avi-Itzhak and Heyman 1973). Important examples of this research include the work of Heyman and Kneale T. Marshall on the optimal control of queues when costs are incurred for turning servers on and o and for delaying customers (Heyman 1968, Heyman and Marshall 1968, Heyman 1977b, and the work of Segal and Halÿn on queuing models involving mixtures of several types of arriving customers (Halÿn andSegal 1972, Halÿn 1972b).…”