Hospital diagnostic facilities, such as magnetic resonance imaging centers, typically provide service to several diverse patient groups: outpatients, who are scheduled in advance; inpatients, whose demands are generated randomly during the day; and emergency patients, who must be served as soon as possible. Our analysis focuses on two interrelated tasks: designing the outpatient appointment schedule, and establishing dynamic priority rules for admitting patients into service.

We formulate the problem of managing patient demand for diagnostic service as a finite-horizon dynamic program and identify properties of the optimal policies. Using empirical data from a major urban hospital, we conduct numerical studies to develop insights into the sensitivity of the optimal policies to the various cost and probability parameters and to evaluate the performance of several heuristic rules for appointment acceptance and patient scheduling.

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Managing Patient Service in a Diagnostic Medical Facility

The problem of packing a knapsack of integer volume F with objects from K different classes to maximize profit is studied. Optimization is carried out over the class of coordinate convex policies. For the case of K=2, it is shown for a wide range of parameters that the optimal control is of the threshold type. In the case of Poisson arrivals and of knapsack and object volumes being integer multiples of each other, it is shown that the optimal policy is always of the double-threshold type. An O(F) algorithm to determine the revenue of threshold policies is also given. For the general case of K classes, the problem of the optimal static control where for each class a portion of the knapsack is dedicated is considered. An efficient finite-stage dynamic programming algorithm for locating the optimal static control is presented. Furthermore, variants of the optimal static control which allow some sharing among classes are also discussed. >

The stochastic knapsack problem

Stochastic knapsack problem

Buffer management schemes are needed to fairly regulate the sharing of memory among different output port queues in a shared memory ATM switch. Of the conventional schemes, static threshold is simple but does not adapt to changing traffic conditions while pushout is efficient and adaptive but difficult to implement. We propose a novel scheme called dynamic threshold which combines the simplicity of static threshold and the adaptability of pushout. The key idea is that the maximum permissible length, for any individual queue at any instant of time, is proportional to the unused buffering in the switch. A queue whose length equals or exceeds the current threshold value may accept no more new cells. The dynamic threshold procedure presented improves the fairness and switch efficiency by guaranteeing access to the buffer space for all output queues. Computer simulation is used to compare the loss performance of the dynamic threshold technique with that of static threshold and pushout. The dynamic threshold scheme is shown to be a good compromise: while nearly as simple as static threshold control, it offers most of the performance benefits of pushout. Like pushout, the dynamic threshold method is adaptive, so it is more robust to uncertainties and changes in traffic conditions than, static threshold control.

Dynamic queue length thresholds in a shared memory ATM switch

In shared-memory packet switches, buffer management schemes can improve overall loss performance, as well as fairness, by regulating the sharing of memory among the different output port queues. Of the conventional schemes, static threshold (ST) is simple but does not adapt to changing traffic conditions, while pushout (PO) is highly adaptive but difficult to implement. We propose a novel scheme called dynamic threshold (DT) that combines the simplicity of ST and the adaptivity of PO. The key idea is that the maximum permissible length, for any individual queue at any instant of time, is proportional to the unused buffering in the switch. A queue whose length equals or exceeds the current threshold value may accept no more arrivals. An analysis of the DT algorithm shows that a small amount of buffer space is (intentionally) left unallocated, and that the remaining buffer space becomes equally distributed among the active output queues. We use computer simulation to compare the loss performance of DT, ST, and PO. DT control is shown to be more robust to uncertainties and changes in traffic conditions than ST control.

Dynamic queue length thresholds for shared-memory packet switches

Efficient design of service facilities, such as data or computer networks that meet random demands, often leads to the sharing of resources among users. Contention for the use of a resource results in queueing. The waiting room is a part of any such service facility. The number of accepted service requests per unit of time (throughput), or the fraction of the time the servers are busy (utilization), are often used as performance measures to compare designs. Most common models in queueing theory consider the design of the waiting rooms with the assumption that, although individual requests may differ from one another, they are statistically indistinguishable. However, there are several instances where available information allows us to classify the requests for service into different types. In such cases the design of the service facility not only involves the determination of an optimum size for the waiting room but also the rules of sharing it among the different types. Even with a fixed set of resources, the rules of sharing them can influence performance. In data networks (or computer networks) the "waiting room" consists of memory of one kind or another. Messages (jobs) destined for different locations (processors) sharing common storage is an important example of shared use of memory. Recently, Kleinrock and Kamoun have modeled such use of memory and computed the performance of various policies for managing the allocation of memory to several types of users. Decisions to accept or reject a demand for service were based on the number of waiting requests of each type. However, the optimal policy was not determined even in the case where there were only two types of users. We determine the structure of optimal policies for the model considered with three types of users. The optimal policy consists of limiting the number of waiting requests of each type, and reserving a part of the memory to each type.

B. Gopinath

Papers

Sharing Memory Optimally