scholarly journals Queue-length balance equations in multiclass multiserver queues and their generalizations

2017 ◽  
Vol 86 (3-4) ◽  
pp. 277-299 ◽  
Author(s):  
Marko A. A. Boon ◽  
Onno J. Boxma ◽  
Offer Kella ◽  
Masakiyo Miyazawa
Keyword(s):  
Queue Length ◽  
Balance Equations ◽  
Multiserver Queues

Asymptotic exponentiality of the tail of the waiting-time distribution in a Ph/Ph/C queue

1981 ◽  
Vol 13 (03) ◽  
pp. 619-630 ◽  
Author(s):  
Yukio Takahashi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Queue Length ◽  
Time Distribution ◽  
Length Distribution ◽  
Waiting Time Distribution ◽  
Queue Length Distribution ◽  
Multiserver Queues ◽  
The Matrix ◽  
Rates Of Decay

It is shown that, in a multiserver queue with interarrival and service-time distributions of phase type (PH/PH/c), the waiting-time distributionW(x) has an asymptotically exponential tail, i.e., 1 –W(x) ∽Ke–ckx. The parameter k is the unique positive number satisfyingT*(ck)S*(–k) = 1, whereT*(s) andS*(s) are the Laplace–Stieltjes transforms of the interarrival and the service-time distributions. It is also shown that the queue-length distribution has an asymptotically geometric tail with the rate of decay η =T*(ck). The proofs of these results are based on the matrix-geometric form of the state probabilities of the system in the steady state.The equation for k shows interesting relations between single- and multiserver queues in the rates of decay of the tails of the waiting-time and the queue-length distributions.The parameters k and η can be easily computed by solving an algebraic equation. The multiplicative constantKis not so easy to compute. In order to obtain its numerical value we have to solve the balance equations or estimate it from simulation.

Queueing networks by negative customers and negative queue lengths

1993 ◽  
Vol 30 (04) ◽  
pp. 931-942 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Equilibrium Distribution ◽  
State Dependence ◽  
Balance Equations ◽  
Negative Customers ◽  
Jackson Networks ◽  
Geometric Product ◽  
Queue Lengths ◽  
Number Of Customers

A number of papers have recently appeared in the literature in which customers, in moving from node to node in the network arrive as either a positive customer or as a batch of negative customers. A positive customer joining its queue increases the number of customers at the queue by 1 and each negative customer decreases the queue length by 1, if possible. It has been shown that the equilibrium distribution for these networks assumes a geometric product form, that certain partial balance equations prevail and that the parameters of the geometric distributions are, as in Jackson networks, the service facility throughputs of customers. In this paper the previous work is generalised by allowing state dependence into both the service and routing intensities and by allowing the possibility, although not the necessity, for negative customers to build up at the nodes.

Queueing networks by negative customers and negative queue lengths

1993 ◽  
Vol 30 (4) ◽  
pp. 931-942 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Queueing Networks ◽  
Queue Length ◽  
Equilibrium Distribution ◽  
State Dependence ◽  
Balance Equations ◽  
Negative Customers ◽  
Jackson Networks ◽  
Geometric Product ◽  
Queue Lengths ◽  
Number Of Customers

A number of papers have recently appeared in the literature in which customers, in moving from node to node in the network arrive as either a positive customer or as a batch of negative customers. A positive customer joining its queue increases the number of customers at the queue by 1 and each negative customer decreases the queue length by 1, if possible. It has been shown that the equilibrium distribution for these networks assumes a geometric product form, that certain partial balance equations prevail and that the parameters of the geometric distributions are, as in Jackson networks, the service facility throughputs of customers. In this paper the previous work is generalised by allowing state dependence into both the service and routing intensities and by allowing the possibility, although not the necessity, for negative customers to build up at the nodes.

Asymptotic exponentiality of the tail of the waiting-time distribution in a Ph/Ph/C queue

1981 ◽  
Vol 13 (3) ◽  
pp. 619-630 ◽  
Author(s):  
Yukio Takahashi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Queue Length ◽  
Time Distribution ◽  
Length Distribution ◽  
Waiting Time Distribution ◽  
Queue Length Distribution ◽  
Multiserver Queues ◽  
The Matrix ◽  
Rates Of Decay

It is shown that, in a multiserver queue with interarrival and service-time distributions of phase type (PH/PH/c), the waiting-time distribution W(x) has an asymptotically exponential tail, i.e., 1 – W(x) ∽ Ke–ckx. The parameter k is the unique positive number satisfying T*(ck) S*(–k) = 1, where T*(s) and S*(s) are the Laplace–Stieltjes transforms of the interarrival and the service-time distributions. It is also shown that the queue-length distribution has an asymptotically geometric tail with the rate of decay η = T*(ck). The proofs of these results are based on the matrix-geometric form of the state probabilities of the system in the steady state.The equation for k shows interesting relations between single- and multiserver queues in the rates of decay of the tails of the waiting-time and the queue-length distributions.The parameters k and η can be easily computed by solving an algebraic equation. The multiplicative constant K is not so easy to compute. In order to obtain its numerical value we have to solve the balance equations or estimate it from simulation.

Effects of Ambipolar Diffusion on Prominence Thread Models

1994 ◽  
Vol 144 ◽  
pp. 315-321 ◽  
Author(s):  
M. G. Rovira ◽  
J. M. Fontenla ◽  
J.-C. Vial ◽  
P. Gouttebroze
Keyword(s):  
Energy Balance ◽  
Transition Region ◽  
Ambipolar Diffusion ◽  
Line Profiles ◽  
Balance Equations ◽  
Model Calculations ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Theoretical Structure

AbstractWe have improved previous model calculations of the prominence-corona transition region including the effect of the ambipolar diffusion in the statistical equilibrium and energy balance equations. We show its influence on the different parameters that characterize the resulting prominence theoretical structure. We take into account the effect of the partial frequency redistribution (PRD) in the line profiles and total intensities calculations.

Parametric Study of Photovoltaic Thermal Solar Collector Using An Improved Parallel Flow

2020 ◽  
Vol 2 (1) ◽  
pp. 19-24
Author(s):  
Sakhr Mohammed Sultan ◽  
Chih Ping Tso ◽  
Ervina Efzan Mohd Noor ◽  
Fadhel Mustafa Ibrahim ◽  
Saqaff Ahmed Alkaff
Keyword(s):  
Thermal Conductivity ◽  
Energy Balance ◽  
Parametric Study ◽  
Solar Collector ◽  
Parallel Flow ◽  
Operating Conditions ◽  
Balance Equations ◽  
Conductivity Type ◽  
Pv Module ◽  
Sunny Weather

Photovoltaic Thermal Solar Collector (PVT) is a hybrid technology used to produce electricity and heat simultaneously. Current enhancements in PVT are to increase the electrical and thermal efficiencies. Many PVT factors such as type of absorber, thermal conductivity, type of PV module and operating conditions are important parameters that can control the PVT performance. In this paper, an analytical model, using energy balance equations, is studied for PVT with an improved parallel flow absorber. The performance is calculated for a typical sunny weather in Malaysia. It was found that the maximum electrical and thermal efficiencies are 12.9 % and 62.6 %, respectively. The maximum outlet water temperature is 59 oC.

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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