Two Classes of Time-Inhomogeneous Markov Chains: Analysis of The Periodic Case

We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is presented

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

In this paper, we consider a discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system. A more flexible switching mechanism between low and regular service states is introduced to enhance the practical value of the working vacation queue. Under different precision levels of the system information, namely observable, almost unobservable and fully unobservable cases, the utility function is studied from both the individual customer’s and the system administrator’s points of view. By analyzing the steady-state behavior of the system, the associated optimal joining decisions under different information scenarios are obtained. We find that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period. A similar situation also appears in almost unobservable case. Such phenomenon is not possible for the classic first come first served queue due to the fact that there is no vacation time and thus will not cause large fluctuations in customers’ conditional waiting time. Additionally, we also conduct some numerical comparisons to demonstrate the effect of the information levels as well as system parameters on customer joining behavior.This research was partially supported by grant from NSERC DAS programs, National Natural Science Foundation of China (Nos.71301111, 71571127, 71402072) and the FSUSE (No.2012RC23).http://www.elsevier.com/locate/caor2017-09-30hb2016Electrical, Electronic and Computer Engineerin

Some analysis results associated with the optimization problem for a discrete-time finite-buffer NT-policy queue

The prime objective of this paperis to give some analysis results concerning the discrete-time finite-buffer NT-policy queue, which can be utilized to determine the optimal threshold values. By recording the waiting time of the leading customer in server’s vacation period, the model is successfully described as a vector-valued Markov chain. Meanwhile, depending on the special block structure of the one-step transition probability matrix, the equilibrium queue length distribution is calculated through a more effective UL-type RG-factorization. Due to the number of customers served in the busy period does not have the structure of a Galton-Watson branching process, analysis of the regeneration cycle is regarded as a difficult problem in establishing the cost structure of the queueing system. However, employing the concept of i-busy period and some difference equation solving skills, the explicit expression for the expected length of the regeneration cycle is easily derived, and the stochastic decomposition structure of the busy period is also demonstrated. Finally, numerical results are offered to illustrate how the direct search method can be implemented to obtain the optimal management policy.This research was partially supported by grant from NSERC DAS programs, National Natural Science Foundation of China (Nos. 71301111,71171138, 71402072) and the FSUSE (No.2012RC23).http://link.springer.com/journal/123512017-07-30hb201

Using lagrangian relaxation for radio resource allocation in high altitude platforms

In this paper, we study radio resource allocation for multicasting in OFDMA based high altitude platforms (HAPs). We formulate and solve an optimization problem that finds the best allocation of HAP resources such as radio power, subchannels, and time slots. The problem also finds the best possible frequency reuse across the cells that constitute the service area of the HAP. The objective is to maximize the number of user terminals that receive the requested multicast streams in the HAP service area in a given OFDMA frame. A bounding subroutine in a branch and bound algorithm can be obtained by decomposing it into two easier subproblems, due to its high complexity, and solving them iteratively. Subproblem1 turns out to be a binary integer linear program of no explicitly noticeable structure and therefore Lagrangian relaxation is used to dualize some constraints to get a structure that is easy to solve. Subproblem 2 turns out to be a linear program with a continuous knapsack problem structure. Hence a greedy algorithm is proposed to solve subproblem 2 to optimality. The subgradient method is used to solve for the dual variables in the dual problem to get the tightest bounds.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7742hb2016Electrical, Electronic and Computer Engineerin

A simple method to obtain the stochastic decomposition structure of the busy period in Geo/Geo/1/N vacation queue

In this paper, some tips and tricks for algebraic manipulations are utilized to explicitly get the mean and variance of the duration of the busy period in a discretetime finite-buffer vacation queue. Applying the law of total expectation, the closedform expressions for the first two moments of the busy period initiated with an arbitrary number of customers are firstly derived. Then, by employing the queue length distri-bution at vacation termination and the quantities that mentioned above, we give the stochastic decomposition structure of the busy period. Finally, in order to ensure the reliability of the analytical approach, an effective way to validate the correctness of our results along with a numerical example is also provided. We may find that these simple tips and tricks can greatly reduce the difficulty of problem solving.This researchwas partially supported by grant from NSERCDAS programs, National Natural Science Foundation of China (Nos. 71301111, 71171138, 71402072) and the FSUSE (No. 2012RC23).http://link.springer.com/journal/102882016-12-31hb2016Electrical, Electronic and Computer Engineerin

An analytical model for molecular propagation in nanocommunication via filaments using relay-enabled nodes

Molecular communication is a nanoscale communication method in which information is encoded in molecules. Molecular communication using microtubules in free space is one of the realistic scenarios proposed for this type of nanocommunication. Based on this technique, molecular communication via filaments using nano-relays is proposed in this paper to improve the performance of the system in terms of delay and bit error probability. An analytical model using jump diffusion processes is proposed for molecular propagation in this scenario. It is shown that the proposed mathematical model is capable of tracking molecular propagation in molecular communication via filaments using nano-relays. Also, the model is used to investigate effects of different parameters on delay and bit error probability.In part of NSERC (the Natural Sciences and Engineering Research Council of Canada).http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7728hb2016Electrical, Electronic and Computer Engineerin

Optimizing radio resources for multicasting on high-altitude platforms

High-altitude platforms (HAPs) are quasi-stationary aerial wireless communications platforms meant to be located in the stratosphere, to provide wireless communications and broadband services. They have the ability to fly on demand to temporarily or permanently serve regions with unavailable infrastructure. In this paper, we consider the development of an efficient method for resource allocation and controlling user admissions to multicast groups in a HAP system. Power, frequency, space and time domains are considered in the problem. The combination of these many aspects of the problem in multicasting over an OFDMA HAP system were not, to the best of our knowledge, addressed before. Due to the strong dependence of the total number of users that could join different multicast groups on the possible ways we may allocate resources to the different multicast groups, it is important to consider a joint user to multicast group assignments and radio resource management across the groups. From the service provider’s point of view, it would be in its best interest to be able to admit as many users as possible, while satisfying their quality of service requirements. The problem turns out to be a mixed integer non-convex non-linear program for which branch and bound solution framework is guaranteed to solve the problem. Branch and bound (BnB) can be also used to obtain sub-optimal solutions with desired quality. Even though branch and bound is guaranteed to find the optimal solution, the computational cost could be extremely high, which is why we considered different types of enhancements to BnB. Mainly, we consider reformulations by linearizing a specific set of quadratic constraints in the derived formulation, as well as the application of different branching techniques to find the one that performs the best. Based on the conducted numerical experiments, it was concluded that linearization, applied for at least 100 presolving rounds, and cloud branching achieve the best performance.The material in this paper is based on part of the PhD thesis of the first author, under the supervision of the second author.The Natural Sciences and Engineering Research Council (NSERC) of Canadahttps://www.hindawi.com/journals/ivpam2020Electrical, Electronic and Computer Engineerin

A coalitional game-based relay load balancing and power allocation scheme in decode-and-forward cellurlar relay networks

In this paper, a game theoretic relay load balancing and power allocationscheme is proposed for downlink transmission in a decode-and-forward orthogonal frequency division multiple access-based cellular relay network. A system with a base station communicating with multiple users via multiple relays is considered. The relays have limited power, which must be divided among the users they support. In traditional scheme, each relay simply divides its transmit power equally among all its users. Moreover, each user selects the relay with the highest channel gain. In this work, we do not apply the traditional relay scheme. It is because the users are distributed randomly, and by applying the traditional relay selection scheme, it may happen that some relays have more users connected to them than other relays, which results in having unbalanced load among the relays. In order to avoid performance degradation, achieve relay load balancing, and maximize the total data rate of the network, a game theoretic approach is proposed, which efficiently assigns the users to relays. The power of each relay is wisely distributed among users by the efficient power allocation scheme. Simulation results indicate that the proposed game-based scheme can considerably improve the average sum-spectral efficiency. Moreover, it shows that by applying the game, users who can connect to uncongested relays join them as opposed to connecting to congested relays.Grant from the Natural Sciences and Engineering Research Council (NSERC) IRC and Bell Canada.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1530-86772017-06-30hb2016Electrical, Electronic and Computer Engineerin

Computational Procedures for a Class of GI/D/ k

A class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures

Queueing analysis of performance measures under a new configurable channel allocation in cognitive radio

To help achieve optimal channel allocation for a cognitive radio network with multiple channels and multiple users, the authors propose an queueing analytical framework for implementing a configurable channel allocation method. Various allocation scenarios can be captured by the allocation method under different parameters. The influence of the parameters under different environmental parameters and system settings on the performance measures is investigated by the proposed framework. System settings such as imperfect spectrum sensing, adaptive modulation and coding scheme, automatic repeat and request, various primary user activity patterns and finite secondary user buffer size are considered to make the proposed model practical. The procedures to derive performance measures, such as average queue length, packet loss rate, throughput and average packet delay, are presented. Numerical results are shown to reveal the relationship between various performance measures and the channel allocation method parameters under different channel conditions and secondary user system settings. The allocation method and the analytical framework would be useful to help achieve optimal performance and evaluate different allocation methods.Sentech Chair in BWMC and DTI THRIP program.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25hj2018Electrical, Electronic and Computer Engineerin