Julian Keilson

A Service System with Unfilled Requests Repeated

The object of this paper is to analyze a model of a queuing system in which customers cannot be in continuous contact with the server, but must call in to request service: If the server is free, then the next request to arrive is served immediately; if the server is occupied, however, the unsatisfied customer must break contact and later re-initiate his request. Thus, repeat requests for service from the pool of unsatisfied customers are superimposed on the normal stream of arrivals of first attempts. This system is characteristic of situations in which there is a single operator or source of information that must be called and busy signals are not held. This paper calculates several characteristic quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first requests and repeat requests.

Blocking probability for M/G/1 vacation systems with occupancy level dependent schedules

An M/G/1 queue with finite buffer capacity and server vacation schedules dependent on occupancy level is studied. The blocking probability is expressed simply in terms of the ergodic queue length probabilities for the infinite buffer case.

Multi-server threshold queues with hysteresis

Abstract A queueing system with K servers operates in the following manner. When the system is empty, arriving customers are attended by only one server. A set of forward threshold values is defined so that at epochs at which the number of customers in the system exceeds a forward threshold value an extra server is added. Similarly, a set of reverse threshold values is defined so that at epochs at which the number of customers in the system becomes less than a reverse threshold value one server is removed. The forward and reverse threshold values are assumed to be different. Closed-form occupancy distribution and mean delay of customers in the system are obtained by the Greens function method.

Cori cycle activity in man

12 subjects have been studied after an overnight fast with trace amounts of pyruvate-3-(14)C and glucose-6-(14)C. Blood disappearance curves and incorporation of the pyruvate-3-(14)C label into blood glucose have been determined. By the use of transfer functions which allow processes with many different chemical steps to be examined as a unit, we have determined the per cent of pyruvate and presumably lactate which is regenerated into glucose. 8 of the 12 subjects showed that 7-23 mg/kg per hr are recycled, while 4 subjects fell well outside this range. Correlation of increased activity was not good with any demonstrated metabolic abnormality (diabetes or obesity), and it is suggested from clinical observation of the subjects that anxiety may play a role.

Dynamics of the M/G/1 Vacation Model

An M/G/1 processor schedule attends to auxiliary vacation tasks iteratively. We describe the influence of these tasks on the dynamic behavior of the system and obtain, for several cases of interest, the relaxation time of the vacation system required to validate steady-state approximations. Finally, we find the distribution of the duration of the primary busy period, the vacation busy period, and an associated cycle time.

Transfer times across the human body

The radioactivity disappearance curves of glucose-6-14C albumin-I131 after a single injection of tracer into a human subject have been determined in detail, particularly at early time intervals. The curves, expressed as sums of exponentials, have been analyzed as the infinite sum of convolutions of single passage time densities. The resultant transfer time distribution of a single circulatory pass allows examination of all delays in the system no matter how long they take. The structural detail evident by this means and the long mean time of a single pass of glucose (>5 min) supports the thesis that factors other than rapid and uniform diffusion play a role in the extravascular movements of glucose molecules.

Cutoff priority scheduling in mobile cellular communication systems

A mobile cellular communication system is considered. The calls arriving at the base station of each cell are modeled by a queueing system with two arrival streams. Stream 1 (also called class 1) arrivals are those calls in progress that are handed over to the cell from other cells, and class a arrivals are those calls that are originating in the cell. The guard channel scheme is considered in which arriving calls are indiscriminately assigned channels within a cell as long as the number of busy channels in the cell is below a predefined threshold. When this number reaches the threshold, only arriving class 1 calls are assigned channels immediately; arriving class 2 calls are queued. When all the channels are busy, then arriving class 1 calls are lost while class 2 calls continue to be queued. The system is analysed by a generating function method which utilizes the structure of the model to give a very concise solution. >

Unimodality preservation in Markov chains

A subset of the stochastically monotone Markov chains has the property that the expectation of unimodal functions of the chain is itself unimodal in the initial state. The variation- diminishing property of TP2 matrices is employed to characterize these Markov chains. Related properties are exhibited.

A circulatory model for human metabolism

Abstract We describe a new circulatory model for the analysis of human metabolic data compatible with the limited information obtainable in clinical studies when only a few metabolites are observed. The model makes no assumptions about intermediary metabolites, which may not be known, the existence of compartments or the size of these compartments. Only observed data are employed. While for a single substance the model provides no new format, the description of the quantitative relationship between two or more substances is unambiguous and precise, and allows considerably more insight than by previous methods. Via the model, direct entry rates into plasma metabolites, the direct departure rates and the conversion rate between two substances, both for first conversion and repetitive conversions, can be established. Specification of the data needed to determine these kinetic relationships is given. For the glucose-alanine system peculiarities present which may require extra steps in data analysis are described. The randomness generated by turbulent mixing in the heart gives the underlying theory a probabilistic character, and much of the methodology has its origins there. The randomness is nullified by the law of large numbers, but the mathematical structure remains.

Dynamic Bandwidth Allocation, Routing, and Access Control in ATM Networks

We propose a layered architecture for adaptive traffic control in ATM networks that utilizes the virtual path (VP) concept. The proposed control guarantees quality of service and simplifies call and cell processing. The control is organized in three levels: a VP level, a virtual circuit (VC) level, and a cell level.