ABSTRACT We consider various inventory, queueing and reliability models where there is apparent c... more ABSTRACT We consider various inventory, queueing and reliability models where there is apparent complexity due to interacting components or subsystems. In particular, our analysis focuses on a multi-item inventory model with stochastically dependent demands, a queueing network where there are dependent arrival and service processes, or a reliability model with stochastically dependent component lifetimes. We discuss cases where this dependence is induced only by a random environmental process which the system operates in. This process represents the sources of variation that affect all deterministic and stochastic parameters of the model. Thus, not only the parameters of the model are now stochastic processes, but they are all dependent due to the common environment they are all subject to. Our objective is to provide a convincing argument that, under fairly reasonable conditions, the analysis techniques used in these models as well their solutions are not much more complicated than those where there is no environmental variation.
International Journal of Production Economics, Aug 1, 2002
We consider a single item inventory model which is observed periodically in a randomly changing e... more We consider a single item inventory model which is observed periodically in a randomly changing environment. All model parameters are specified by the state of the environment which is assumed to be a time-homogeneous Markov chain. Yield is random due to the random capacity of ...
A system subject to catastrophic failure deteriorates according to a delayed Markov process and i... more A system subject to catastrophic failure deteriorates according to a delayed Markov process and is subjected to a series of binary tests that may yield false negative and false positive outcomes. A corrective action is carried out when a true positive is observed, thereby reducing the chance of system failure. Costs of inspections, false positives, the corrective action, and failure are incurred, and dynamic programming is used to compute the optimal inspection schedule. Two tractable computational methods are developed. The model, which is suited for medical screening, is applied to the problems of post-operative periumbilical pruritis and breast cancer.
Stochastic processes in queueing theory elementary queueing models simulation of queueing systems... more Stochastic processes in queueing theory elementary queueing models simulation of queueing systems queueing networks - a survey of analytical results simulation of queueing models in computer systems a perspective on academic computer networking management and optimization of queueing systems queueing network models for flexible manufacturing systems. Part contents only.
In this paper the optimal replacement problem of a one-unit system under periodic inspection is a... more In this paper the optimal replacement problem of a one-unit system under periodic inspection is analyzed utilizing Markov decision theory. The problem is formulated in a general setting and it is shown that an age replacement policy is in fact optimal if the component lifetime has monotone failure rate. A necessary and sufficient condition of optimality together with several characterizations of the optimal policy are presented.
A safety precaution used in rail transportation is to ensure that only one train occupies the tra... more A safety precaution used in rail transportation is to ensure that only one train occupies the track connecting two stations at any time. We consider a train station where passengers arrive according to a prescheduled timetable, and the transportation authority tries to dispatch the trains on their scheduled departure times. However, if the track to the next station is occupied by a preceding train at such a departure instant, then the departure of the next train is delayed, or even cancelled, to achieve safety in transportation. Under such circumstances, the dispatcher may choose to cancel overdelayed trains intentionally so that the succeeding trains can depart on time, or to dispatch some trains with faster speed to decrease service time. We analyze this rail transportation model to identify the relationships between various dispatching strategies, the arrival pattern of the passengers, and the performance measures involving the service delay and passenger waiting time. The steady-state distribution of the service delay is characterized as the solution of a system of linear equations and an explicit computational formula for the average passenger waiting time is derived. Interesting intuitive and counterintuitive examples are also provided in the context of an optimal dispatching problem.
An interesting behavior of customers arriving to a queue for service concerns the manner in which... more An interesting behavior of customers arriving to a queue for service concerns the manner in which they join the queue. The arrival discipline of the customers may be impolite, in the sense that an arriving customer who finds all servers busy may pick a position which is not necessarily at the end of the line. We introduce and discuss in detail such an arrival discipline of sufficient generality which has interesting applications. In particular, we show that the more impolite an arrival discipline is, the bigger is the variance of the waiting time. We also study a special model in more depth to provide simple computational formulas for several performance measures.
Wiley Encyclopedia of Operations Research and Management Science, Feb 15, 2011
The hazard function describes the probabilistic structure of failures in reliability models. It t... more The hazard function describes the probabilistic structure of failures in reliability models. It therefore plays a crucial role in reliability and maintenance of systems that are subject to failures. It is generally assumed to be some deterministic and increasing function of time that explains how a system deteriorates or ages as it is used. In this article, we consider hazard functions that are in fact stochastic. The aim is to demonstrate a variety of cases where this is true and to discuss issues related to computation of system reliability. Most of our discussions focus on stochastic hazard processes generated through modulation via random environments. Keywords: hazard process; reliability and maintenance; random environment; Markov modulation
The determination of optimal software release times constitutes an interesting decision making pr... more The determination of optimal software release times constitutes an interesting decision making problem which involves the stochastic structure of the underlying software reliability model, as well as various cost parameters. There is an apparent tradeoff between testing the software further to improve its reliability, and releasing it for operational use to decrease the costs. We propose and analyze in depth
ABSTRACT We consider various inventory, queueing and reliability models where there is apparent c... more ABSTRACT We consider various inventory, queueing and reliability models where there is apparent complexity due to interacting components or subsystems. In particular, our analysis focuses on a multi-item inventory model with stochastically dependent demands, a queueing network where there are dependent arrival and service processes, or a reliability model with stochastically dependent component lifetimes. We discuss cases where this dependence is induced only by a random environmental process which the system operates in. This process represents the sources of variation that affect all deterministic and stochastic parameters of the model. Thus, not only the parameters of the model are now stochastic processes, but they are all dependent due to the common environment they are all subject to. Our objective is to provide a convincing argument that, under fairly reasonable conditions, the analysis techniques used in these models as well their solutions are not much more complicated than those where there is no environmental variation.
International Journal of Production Economics, Aug 1, 2002
We consider a single item inventory model which is observed periodically in a randomly changing e... more We consider a single item inventory model which is observed periodically in a randomly changing environment. All model parameters are specified by the state of the environment which is assumed to be a time-homogeneous Markov chain. Yield is random due to the random capacity of ...
A system subject to catastrophic failure deteriorates according to a delayed Markov process and i... more A system subject to catastrophic failure deteriorates according to a delayed Markov process and is subjected to a series of binary tests that may yield false negative and false positive outcomes. A corrective action is carried out when a true positive is observed, thereby reducing the chance of system failure. Costs of inspections, false positives, the corrective action, and failure are incurred, and dynamic programming is used to compute the optimal inspection schedule. Two tractable computational methods are developed. The model, which is suited for medical screening, is applied to the problems of post-operative periumbilical pruritis and breast cancer.
Stochastic processes in queueing theory elementary queueing models simulation of queueing systems... more Stochastic processes in queueing theory elementary queueing models simulation of queueing systems queueing networks - a survey of analytical results simulation of queueing models in computer systems a perspective on academic computer networking management and optimization of queueing systems queueing network models for flexible manufacturing systems. Part contents only.
In this paper the optimal replacement problem of a one-unit system under periodic inspection is a... more In this paper the optimal replacement problem of a one-unit system under periodic inspection is analyzed utilizing Markov decision theory. The problem is formulated in a general setting and it is shown that an age replacement policy is in fact optimal if the component lifetime has monotone failure rate. A necessary and sufficient condition of optimality together with several characterizations of the optimal policy are presented.
A safety precaution used in rail transportation is to ensure that only one train occupies the tra... more A safety precaution used in rail transportation is to ensure that only one train occupies the track connecting two stations at any time. We consider a train station where passengers arrive according to a prescheduled timetable, and the transportation authority tries to dispatch the trains on their scheduled departure times. However, if the track to the next station is occupied by a preceding train at such a departure instant, then the departure of the next train is delayed, or even cancelled, to achieve safety in transportation. Under such circumstances, the dispatcher may choose to cancel overdelayed trains intentionally so that the succeeding trains can depart on time, or to dispatch some trains with faster speed to decrease service time. We analyze this rail transportation model to identify the relationships between various dispatching strategies, the arrival pattern of the passengers, and the performance measures involving the service delay and passenger waiting time. The steady-state distribution of the service delay is characterized as the solution of a system of linear equations and an explicit computational formula for the average passenger waiting time is derived. Interesting intuitive and counterintuitive examples are also provided in the context of an optimal dispatching problem.
An interesting behavior of customers arriving to a queue for service concerns the manner in which... more An interesting behavior of customers arriving to a queue for service concerns the manner in which they join the queue. The arrival discipline of the customers may be impolite, in the sense that an arriving customer who finds all servers busy may pick a position which is not necessarily at the end of the line. We introduce and discuss in detail such an arrival discipline of sufficient generality which has interesting applications. In particular, we show that the more impolite an arrival discipline is, the bigger is the variance of the waiting time. We also study a special model in more depth to provide simple computational formulas for several performance measures.
Wiley Encyclopedia of Operations Research and Management Science, Feb 15, 2011
The hazard function describes the probabilistic structure of failures in reliability models. It t... more The hazard function describes the probabilistic structure of failures in reliability models. It therefore plays a crucial role in reliability and maintenance of systems that are subject to failures. It is generally assumed to be some deterministic and increasing function of time that explains how a system deteriorates or ages as it is used. In this article, we consider hazard functions that are in fact stochastic. The aim is to demonstrate a variety of cases where this is true and to discuss issues related to computation of system reliability. Most of our discussions focus on stochastic hazard processes generated through modulation via random environments. Keywords: hazard process; reliability and maintenance; random environment; Markov modulation
The determination of optimal software release times constitutes an interesting decision making pr... more The determination of optimal software release times constitutes an interesting decision making problem which involves the stochastic structure of the underlying software reliability model, as well as various cost parameters. There is an apparent tradeoff between testing the software further to improve its reliability, and releasing it for operational use to decrease the costs. We propose and analyze in depth
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