scholarly journals Mathematical Modeling and Analysis Methodology for Opportunistic Routing in Wireless Multihop Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Wang Dongyang ◽  
Wu Muqing ◽  
Lv Bo ◽  
Liao Wenxing
Keyword(s):  
Length Distribution ◽  
Opportunistic Routing ◽  
Queuing Model ◽  
Modeling And Analysis ◽  
Multihop Network ◽  
Queue Length Distribution ◽  
Analysis Methodology ◽  
Special Cases ◽  
Simulation Results ◽  
Generalized Geometric Distribution

Modeling the forwarding feature and analyzing the performance theoretically for opportunistic routing in wireless multihop network are of great challenge. To address this issue, a generalized geometric distribution (GGD) is firstly proposed. Based on the GGD, the forwarding probability between any two forwarding candidates could be calculated and it can be proved that the successful delivery rate after several transmissions of forwarding candidates is irrelevant to the priority rule. Then, a discrete-time queuing model is proposed to analyze mean end-to-end delay (MED) of a regular opportunistic routing with the knowledge of the forwarding probability. By deriving the steady-state joint generating function of the queue length distribution, MED for directly connected networks and some special cases of nondirectly connected networks could be ultimately determined. Besides, an approximation approach is proposed to assess MED for the general cases in the nondirectly connected networks. By comparing with a large number of simulation results, the rationality of the analysis is validated. Both the analysis and simulation results show that MED varies with the number of forwarding candidates, especially when it comes to connected networks; MED increases more rapidly than that in nondirectly connected networks with the increase of the number of forwarding candidates.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

scholarly journals The BMAP/G/1 vacation queue with queue-length dependent vacation schedule

1998 ◽  
Vol 40 (2) ◽  
pp. 207-221 ◽  
Author(s):  
Yang Woo Shin ◽  
Chareles E. M. Pearce
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Server Vacation ◽  
Batch Markovian Arrival Process ◽  
Queue Length Distribution ◽  
Special Cases ◽  
Number Of Customers

AbstractWe treat a single-server vacation queue with queue-length dependent vacation schedules. This subsumes the single-server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch-Markovian arrival process (BMAP). We derive the queue-length distribution at departure epochs. By using a semi-Markov process technique, we obtain the Laplace-Stieltjes transform of the transient queue-length distribution at an arbitrary time point and its limiting distribution

Open networks of queues: their algebraic structure and estimating their transient behavior

1984 ◽  
Vol 16 (1) ◽  
pp. 176-201 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Length Distribution ◽  
Transient Behavior ◽  
Product Form ◽  
General Distribution ◽  
Service Discipline ◽  
Operator Representation ◽  
Open Networks ◽  
Queue Length Distribution ◽  
Special Cases ◽  
To Receive

We develop the mathematical machinery in this paper to construct a very general class of Markovian network queueing models. Each node has a heterogeneous class of customers arriving at their own Poisson rate, ultimately to receive their own exponential service requirements. We add to this a very general type of service discipline as well as class (node) switching. These modifications allow us to model in the limit, service with a general distribution. As special cases for this model, we have the product-form networks formulated by Kelly, as well as networks with priority scheduling. For the former, we give an algebraic proof of Kelly's results for product-form networks. This is an approach that motivates the form of the solution, and justifies the various needs of local and partial balance conditions.For any network that belongs to this general model, we use the operator representation to prove stochastic dominance results. In this way, we can take the transient behavior for very complicated networks and bound its joint queue-length distribution by that for M/M/1queues.

An N-policy discrete-time Geo/G/1 queue with modified multiple server vacations and Bernoulli feedback*

2019 ◽  
Vol 53 (2) ◽  
pp. 367-387
Author(s):  
Shaojun Lan ◽  
Yinghui Tang
Keyword(s):  
Discrete Time ◽  
Queue Length ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Renewal Theory ◽  
Function Technique ◽  
Single Server ◽  
Bernoulli Feedback ◽  
Queue Length Distribution ◽  
Special Cases

This paper deals with a single-server discrete-time Geo/G/1 queueing model with Bernoulli feedback and N-policy where the server leaves for modified multiple vacations once the system becomes empty. Applying the law of probability decomposition, the renewal theory and the probability generating function technique, we explicitly derive the transient queue length distribution as well as the recursive expressions of the steady-state queue length distribution. Especially, some corresponding results under special cases are directly obtained. Furthermore, some numerical results are provided for illustrative purposes. Finally, a cost optimization problem is numerically analyzed under a given cost structure.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (1) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

scholarly journals On the Discrete-TimeGeo/G/1Queue with Vacations in Random Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Jianjun Li ◽  
Liwei Liu
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Queue Length Distribution ◽  
Special Cases ◽  
Sojourn Time Distribution ◽  
Stationary Queue Length Distribution ◽  
Number Of Customers ◽  
Mean Time

A discrete-timeGeo/G/1queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also derived. And we present the various performance measures such as mean number of customers in the system, mean length of the type-icycle, and mean time that the system resides in phase0. In addition, we show that theM/G/1queue with vacations in random environment can be approximated by its discrete-time counterpart. Finally, we present some special cases of the model and numerical examples.

Open networks of queues: their algebraic structure and estimating their transient behavior

1984 ◽  
Vol 16 (01) ◽  
pp. 176-201 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Length Distribution ◽  
Transient Behavior ◽  
Product Form ◽  
General Distribution ◽  
Service Discipline ◽  
Operator Representation ◽  
Open Networks ◽  
Queue Length Distribution ◽  
Special Cases ◽  
To Receive

We develop the mathematical machinery in this paper to construct a very general class of Markovian network queueing models. Each node has a heterogeneous class of customers arriving at their own Poisson rate, ultimately to receive their own exponential service requirements. We add to this a very general type of service discipline as well as class (node) switching. These modifications allow us to model in the limit, service with a general distribution. As special cases for this model, we have the product-form networks formulated by Kelly, as well as networks with priority scheduling. For the former, we give an algebraic proof of Kelly's results for product-form networks. This is an approach that motivates the form of the solution, and justifies the various needs of local and partial balance conditions. For any network that belongs to this general model, we use the operator representation to prove stochastic dominance results. In this way, we can take the transient behavior for very complicated networks and bound its joint queue-length distribution by that for M/M/1queues.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

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