Birth-Death Process
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Backward Chaining
Backward-Recurrence Time
An approach to reasoning in which an inference engine endeavors to find a value for an overall goal by recursively finding values for subgoals. At any point in the recursion, the effort of finding a value for the immediate goal involves examining rule conclusions to identify those rules that could possibly establish a value for that goal. An unknown variable in the premise of one of these candidate rules becomes a new subgoal for recursion purposes.
Suppose events occur at times T1, T2, . . . such that the interevent times Tk Tk1 are mutually independent, positive random variables with a common cumulative distribution function. Choose an arbitrary time t. The backward recurrence time at t is the elapsed time since the most recent occurrence of an event prior to t.
See
Balance Equations
▶ Expert Systems
(1) In probability modeling, steady-state systems of equations for the state probabilities of a stochastic process found by equating transition rates. For Markov chains, such equations can be derived from the Kolmogorov differential equations or from the fact that the flow rate into a system state or level must equal the rate out of that state or level for steady state to be achieved. (2) In linear programming (usually referring to a production process model), constraints that express the equality of inflows and outflows of material.
Backward Kolmogorov Equations In a continuous-time Markov chain with state X(t) at time t, define pij(t) as the probability that X(t + s) ¼ j, given that X(s) ¼ i, s, t 0, and rij as the transition rate out of state i to state j. Then Kolmogorov’s backward equations say that, for all states i, j and times t 0, the P derivatives dpij(t)/dt ¼ pij(t), k6¼i rik pkj (t) viP where vi is the transition rate out of state i, vi ¼ j rij.
See See ▶ Markov Chains ▶ Markov Processes
▶ Markov Chains
S.I. Gass, M.C. Fu (eds.), Encyclopedia of Operations Research and Management Science, DOI 10.1007/978-1-4419-1153-7, # Springer Science+Business Media New York 2013
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Balking
Pricing Contingent Cashflows
Balking When customers arriving at a queueing system decide not to join the line and instead go away because they anticipate too long a wait.
See ▶ Queueing Theory
Bandit Model ▶ Multi-armed Bandit Problem
Banking Stavros A. Zenios University of Cyprus, Nicosia, Cyprus University of Pennsylvania, Pennsylvania, PA, USA
Introduction OR/MS techniques find applications in numerous and diverse areas of operation in a banking institution. Applications include the use of data-driven models to measure the operating efficiency of bank branches through data envelopment analysis, the use of image recognition techniques for check processing, the use of artificial neural networks for evaluating loan applications, and the use of facility location theory for opening new branches and placing automatic teller machines (e.g., Harker and Zenios 1999). A primary area of application is that of financial risk control in developing broad asset/liability
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