On the input and output processes for a general birth-and-death queueing model

1975 ◽  
Vol 7 (03) ◽  
pp. 576-592 ◽  
Author(s):  
Bent Natvig
Keyword(s):  
Steady State ◽  
Arrival Rate ◽  
Queueing Model ◽  
System State ◽  
Input And Output ◽  
Service Completion ◽  
First Case ◽  
Inputs And Outputs

The steady-state input and output processes are considered for a birth-and-death queueing model with N waiting positions (0 ≦ N ≦ ∞), s servers (1 ≦ s ≦ ∞) and an arbitrary queueing discipline. Let an index n indicate that the quantity in question depends on the system state but not on time t. The instantaneous arrival rate is λ, the probability of balking (i.e., not trying to obtain service) being ξ n. The instantaneous departure rate, μn , of customers having joined the system is the sum of the rate of service completions and the rate of defections before service completion. Three cases are considered. We start by ignoring balking customers; in the first case treating a lost customer neither as an input nor as an output, then secondly as both. Finally, balking and lost customers are considered both as inputs and outputs.

On the input and output processes for a general birth-and-death queueing model

1975 ◽  
Vol 7 (3) ◽  
pp. 576-592 ◽  
Author(s):  
Bent Natvig
Keyword(s):  
Steady State ◽  
Arrival Rate ◽  
Queueing Model ◽  
System State ◽  
Input And Output ◽  
Service Completion ◽  
First Case ◽  
Inputs And Outputs

The steady-state input and output processes are considered for a birth-and-death queueing model with N waiting positions (0 ≦ N ≦ ∞), s servers (1 ≦ s ≦ ∞) and an arbitrary queueing discipline. Let an index n indicate that the quantity in question depends on the system state but not on time t. The instantaneous arrival rate is λ, the probability of balking (i.e., not trying to obtain service) being ξn. The instantaneous departure rate, μn, of customers having joined the system is the sum of the rate of service completions and the rate of defections before service completion. Three cases are considered. We start by ignoring balking customers; in the first case treating a lost customer neither as an input nor as an output, then secondly as both. Finally, balking and lost customers are considered both as inputs and outputs.

scholarly journals On the reversibility of the input and output processes for a general birth-and-death queueing model

1977 ◽  
Vol 14 (04) ◽  
pp. 876-883 ◽  
Author(s):  
Bent Natvig
Keyword(s):  
Steady State ◽  
Queueing Model ◽  
Input And Output ◽  
First Case ◽  
State Behaviour ◽  
Steady State Behaviour

In this paper we consider the general birth-and-death queueing model of Natvig (1975). Define the input and output processes by the steady-state behaviour of respectively successive input and output intervals. Ignoring balking customers, two cases are considered. In the first case we treat a lost customer neither as an input nor as an output, then secondly as both. For both cases we show the input and output processes to be reverse processes. One mistake and two erroneous comments in Natvig (1975) are also corrected.

scholarly journals On the reversibility of the input and output processes for a general birth-and-death queueing model

1977 ◽  
Vol 14 (4) ◽  
pp. 876-883 ◽  
Author(s):  
Bent Natvig
Keyword(s):  
Steady State ◽  
Queueing Model ◽  
Input And Output ◽  
First Case ◽  
State Behaviour ◽  
Steady State Behaviour

In this paper we consider the general birth-and-death queueing model of Natvig (1975). Define the input and output processes by the steady-state behaviour of respectively successive input and output intervals. Ignoring balking customers, two cases are considered. In the first case we treat a lost customer neither as an input nor as an output, then secondly as both. For both cases we show the input and output processes to be reverse processes. One mistake and two erroneous comments in Natvig (1975) are also corrected.

scholarly journals Holographic quantum tasks with input and output regions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alex May
Keyword(s):  
Bulk Region ◽  
Link Type ◽  
Input And Output ◽  
Quantum Computations ◽  
Inputs And Outputs

Abstract Quantum tasks are quantum computations with inputs and outputs occurring at specified spacetime locations. Considering such tasks in the context of AdS/CFT has led to novel constraints relating bulk geometry and boundary entanglement. In this article we consider tasks where inputs and outputs are encoded into extended spacetime regions, rather than the points previously considered. We show that this leads to stronger constraints than have been derived in the point based setting. In particular we improve the connected wedge theorem, appearing earlier in arXiv:1912.05649, by finding a larger bulk region whose existence implies large boundary correlation. As well, we show how considering extended input and output regions leads to non-trivial statements in Poincaré-AdS2+1, a setting where the point-based connected wedge theorem is always trivial.

Prognostication of system-state in lead-free electronics equipment under cyclic and steady-state thermo-mechanical loads

2009 ◽  
Vol 49 (8) ◽  
pp. 825-838 ◽  
Author(s):  
Pradeep Lall ◽  
Madhura Hande ◽  
Chandan Bhat ◽  
Vikrant More ◽  
Rahul Vaidya
Keyword(s):  
Steady State ◽  
Lead Free ◽  
System State ◽  
Mechanical Loads

scholarly journals A M/M/1 Queueing Network with Classical Retrial Policy

2021 ◽  
Vol 12 (1S) ◽  
pp. 329-337
Author(s):  
S. Shanmugasundaram, Et. al.
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing Network ◽  
State Probability ◽  
Queueing Model ◽  
Steady State Probability ◽  
Numerical Examples ◽  
System Length ◽  
Number Of Customers ◽  
Little's Formula

In this paper we study the M/M/1 queueing model with retrial on network. We derive the steady state probability of customers in the network, the average number of customers in the all the three nodes in the system, the queue length, system length using little’s formula. The particular case is derived (no retrial). The numerical examples are given to test the correctness of the model.

COST ANALYSIS OF THE R-UNRELIABLE-UNLOADER QUEUEING SYSTEM

2008 ◽  
Vol 25 (01) ◽  
pp. 57-73
Author(s):  
KUO-HSIUNG WANG ◽  
CHUN-CHIN OH ◽  
JAU-CHUAN KE
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Queueing System ◽  
Cost Model ◽  
Analytic Solutions ◽  
Queueing Model ◽  
Exponential Distributions ◽  
System Parameters ◽  
Optimal Values ◽  
The Cost

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

Dynamic System Identification Using a Step Input

2005 ◽  
Vol 24 (2) ◽  
pp. 125-134
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
System Identification ◽  
Transfer Function ◽  
Step Response ◽  
Output Data ◽  
Mass System ◽  
Input And Output ◽  
Rational Transfer ◽  
Line Identification ◽  
The Moment

In this paper, we propose a deterministic off-line identification method performed by using input and output data with a constant steady state output response such as a step response that causes noise or vibration from a mechanical system at the moment when it is applied but they are attenuated asymptotically. The method can directly acquire any order of reduced model without knowing the real order of a plant, in such a way that the intermediate parameters are uniquely determined so as to be orthogonal with respect to 0 ∼ N-tuple integral values of output error and irrelevant to the unmodelled dynamics. From the intermediate parameters, the coefficients of a rational transfer function are calculated. In consequence, the method can be executed for any plant without knowing or estimating its order at the beginning. The effectiveness of the method is illustrated by numerical simulations and also by applying it to a 2-mass system.

Model Order Identification of Combustion Instability Using Lipschitz Indices

2019 ◽  
Author(s):  
Salil Harris ◽  
Aniruddha Sinha ◽  
Sudarshan Kumar
Keyword(s):  
Active Control ◽  
Combustion Instability ◽  
Nonlinear Function ◽  
Model Structure ◽  
Control Methods ◽  
Nonlinear Functions ◽  
Lean Premixed Combustion ◽  
Input And Output ◽  
Inputs And Outputs

Abstract Gas turbine combustors employing lean premixed combustion are prone to combustion instability. Combustion instability, if unchecked, will have deleterious effects to the combustor and hence needs to be controlled. Active control methods are preferred to obtain better off-design performance. The effectiveness of active control methods is dependent on the quality of controller which in-turn depends on the quality of model. In the present work, an input-output model structure, where the output of the system at the current instant is modelled as a nonlinear function of delayed inputs and outputs is chosen. As there are infinite possibilities for representation of nonlinear functions, all parameters in the model structure like time delay between input and output, number of delayed input and output terms and the appropriate form of nonlinear function can be obtained only iteratively. However, prior knowledge of delay and number of delayed inputs and outputs reduces the computational intensity. To this end, the present work utilizes the method of Lipschitz indices to obtain the number of delayed inputs and outputs.

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