Asymptotic Results for Buffer Systems under Heavy Load

1987 ◽  
Vol 1 (3) ◽  
pp. 327-348 ◽  
Author(s):  
J. C. W. Van Ommeren ◽  
A. G. de Kok
Keyword(s):  
Load Factor ◽  
Finite Capacity ◽  
Asymptotic Results ◽  
Heavy Load ◽  
Storage Model ◽  
Long Run ◽  
Overflow Probability ◽  
Excess Amount ◽  
Impatient Customer ◽  
Customer Model

This paper considers a dam (or storage) model of the GI/G/I type with a finite capacity K. An arriving input being larger than the unfilled capacity of the dam causes an overflow where the excess amount is lost. Important performance measures for this system are the overflow probability and the long-run fraction of input that is lost. We give asymptotic expansions for these measures for large K both for the case of a load factor less than 1 and for the case of a load factor larger than 1. Also, related results are obtained for the impatient customer model of the M/G/l type.

Cell loss probability for M/G/1 and time-slotted queues

2000 ◽  
Vol 37 (04) ◽  
pp. 1149-1156
Author(s):  
David McDonald ◽  
François Théberge
Keyword(s):  
Continuous Time ◽  
Time Slot ◽  
Arrival Rate ◽  
Cell Loss ◽  
Loss Probability ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Overflow Probability ◽  
The Mean

It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1-ρ)/ρ, where ρ is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1-ρ.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (01) ◽  
pp. 20-37 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Optimal Policy ◽  
Queueing System ◽  
Sufficient Conditions ◽  
System Capacity ◽  
Average Reward ◽  
Finite Capacity ◽  
Long Run ◽  
Optimal Policies ◽  
Service Rates ◽  
Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL

1999 ◽  
Vol 13 (3) ◽  
pp. 309-327 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Admission Control ◽  
Queueing System ◽  
Average Reward ◽  
Objective Functions ◽  
Finite Capacity ◽  
Long Run ◽  
Blackwell Optimality ◽  
Optimal Policies ◽  
Bias Optimality ◽  
Long Run Average Reward

We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is, the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently. Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic, optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.

A storage model in which the net growth-rate is a Markov chain

1972 ◽  
Vol 9 (01) ◽  
pp. 129-139 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Rate Of Change ◽  
Continuous Time Markov Chain ◽  
Finite Capacity ◽  
Storage Model ◽  
Finite State ◽  
Net Growth Rate ◽  
The Times ◽  
Finite State Space

The distribution of the times to first emptiness and first overflow, together with the limiting distribution of content are determined for a dam of finite capacity. It is assumed that the rate of change of the level of the dam is a continuous-time Markov chain with finite state-space (suitably modified when the dam is full or empty).

TECHNICAL EVALUATION OF A RUNWAY USING THE DEFLECTION METHOD

Aviation ◽  
2013 ◽  
Vol 17 (4) ◽  
pp. 150-160 ◽  
Author(s):  
Devinder K. Yadav ◽  
Hamid Nikraz
Keyword(s):  
Civil Aviation ◽  
Load Factor ◽  
Runway Performance ◽  
Heavy Load ◽  
International Civil Aviation Organisation ◽  
Pavement Evaluation ◽  
Technical Evaluation ◽  
Touchdown Point ◽  
Mechanical Elements ◽  
Semi Empirical

An aircraft imposes a heavy load on a runway during landing, resulting in deflection of the runway pavement. Therefore, runway performance is influenced by potential deflection levels. Estimating deflection at touch-down point is a challenging task, however. Generally, the applied load depends on the weight and vertical velocity of the aircraft before hitting the touchdown point. Similarly, performance of runway pavement is influenced by many factors such as number of landings, load factor, soil characteristics, etc. This study discusses landing practices, imposed load analysis, and runway pavement evaluation. The study is based on the idealisation of runway characteristics using mechanical elements, and it suggests that the mechanical modelling approach can be applied to estimate runway deflection. As a result, the analytically predicted deflection findings instead of the semi-empirical practices currently followed by various states of the International Civil Aviation Organisation (hereinafter – ICAO) can be used to carry out technical evaluation of a runway pavement.

A storage model in which the net growth-rate is a Markov chain

1972 ◽  
Vol 9 (1) ◽  
pp. 129-139 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Rate Of Change ◽  
Continuous Time Markov Chain ◽  
Finite Capacity ◽  
Storage Model ◽  
Finite State ◽  
Net Growth Rate ◽  
The Times ◽  
Finite State Space

The distribution of the times to first emptiness and first overflow, together with the limiting distribution of content are determined for a dam of finite capacity. It is assumed that the rate of change of the level of the dam is a continuous-time Markov chain with finite state-space (suitably modified when the dam is full or empty).

On a generalized finite-capacity storage model

1983 ◽  
Vol 20 (3) ◽  
pp. 663-674 ◽  
Author(s):  
Samuel W. Woolford
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
State Space ◽  
Random Variables ◽  
Time Dependent ◽  
Finite Capacity ◽  
Random Input ◽  
Storage Model ◽  
Limit Distributions

This paper considers a finite-capacity storage model defined on a Markov chain {Xn; n = 0, 1, ·· ·}, having state space J ⊆ {1, 2, ·· ·}. If Xn = j, then there is a random ‘input' Vn(j) (a negative input implying a demand) of ‘type' j, having a distribution function Fj(·). We assume that {Vn(j)} is an i.i.d. sequence of random variables, taken to be independent of {Xn} and of {Vn (k)}, for k ≠ j. Here, the random variables Vn(j) represent instantaneous ‘inputs' of type j for our storage model. Within this framework, we establish certain limit distributions for the joint processes (Zn, Xn) and (Zn, Qn, Ln), where Zn (defined in (1.2)) is the level of storage at time n, Qn (defined in (1.3)) is the cumulative overflow at time n, and Ln (defined in (1.4)) is the cumulative demand lost due to shortage of supply up to time n. In addition, an expression for the time-dependent distribution of (Zn, Xn) is obtained.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (1) ◽  
pp. 20-37 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Optimal Policy ◽  
Queueing System ◽  
Sufficient Conditions ◽  
System Capacity ◽  
Average Reward ◽  
Finite Capacity ◽  
Long Run ◽  
Optimal Policies ◽  
Service Rates ◽  
Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

Storage with deterministic outputs and inputs subject to breakdown

1968 ◽  
Vol 5 (03) ◽  
pp. 636-647 ◽  
Author(s):  
P. M. Wu
Keyword(s):  
Finite Capacity ◽  
Minimum Level ◽  
Secondary Products ◽  
Storage Model ◽  
Operational System ◽  
Whole Process ◽  
Storage Problem

In this paper, we shall consider a storage model in which a bin of finite capacity is fed by specified r(r > 0) or zero input depending on the content of the bin and the operation of the input machines (i.e., whether or not they are working on the bin). These machines are allowed to fill the bin until its level reaches maximum and they are then used to produce some secondary products not relevant to the storage problem. When the content of the bin decreases to a given minimum level, these machines are again set to feed the bin. The whole process is then repeated. It is often desirable in practice to keep the minimum level as low as possible, to attain stability in the process, or for maintenance purposes. When the machines are subject to breakdowns, it becomes necessary to consider the reliability of the operational system.

Characterization of the optimal class of output policies in a control model of a finite dam

1981 ◽  
Vol 18 (04) ◽  
pp. 913-923
Author(s):  
Dror Zuckerman
Keyword(s):  
Wiener Process ◽  
Control Model ◽  
Finite Capacity ◽  
Output Rate ◽  
Optimal Output ◽  
Long Run ◽  
Finite Dam

In this paper we characterize the optimal class of output policies in a control model of a dam having a finite capacity. The input of water into the dam is determined by a Wiener process with positive drift. Water may be released at either of two possible rates 0 or M. At any time the output rate can be increased from 0 to M with a cost of K, (K ≧ 0) or decreased from M to 0 with zero cost, any such changes taking effect instantaneously. There is a reward of A monetary units for each unit of output, (A ≧ 0). The problem is to formulate an optimal output policy which maximizes the long-run average net reward per unit time.

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