Infinite Buffer Size Research Articles

Minimizing Age-Upon-Decisions in Bufferless System: Service Scheduling and Decision Interval

The data freshness at decision epochs of time-sensitive applications, e.g., auto-driving vehicles and autonomous underwater robots, is jointly affected by the statistics of update process and decision process. This work considers an update-and-decision system with a Poisson-arrival bufferless queue, where updates are delivered and processed for making decisions with exponential or periodic intervals. We use age-upon-decisions (AuD) to characterize timeliness of updates at decision moments, and the missing probability to specify whether updates are useful for decision-making. Our theoretical analyses 1) present the average AuDs and the missing probabilities for bufferless systems with exponential or deterministic decision intervals under different service time distributions; 2) show that for service scheduling, the deterministic service time achieves a lower average AuD and a smaller missing probability than the uniformly distributed and the negative exponentially distributed service time; 3) prove that the average AuD of periodical decision system is larger than and will eventually drop to that of Poisson decision system along with the increase of decision rate; however, the missing probability in periodical decision system is smaller than that of Poisson decision system. The numerical results and simulations verify the correctness of our analyses, and demonstrate that the bufferless systems outperform the systems applying infinite buffer size.

On the Stochastic Analysis of a Quantum Entanglement Distribution Switch

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate to use a discrete-time Markov chain (DTMC) to model such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

Secure Communication With Energy-Harvesting Buffer-Aided Jammer

Information security and self-sustainability are crucial to resource-limited wireless networks. In this paper, we assess the secrecy performance of the legitimate link without having eavesdropper's channel state information (CSI) while considering an energy harvesting (EH) jammer with finite and infinite energy buffer sizes. The EH jammer utilizes accumulated energy from its buffer and transmits artificial noise (AN) to ensure secure communication. To manage the uncertainty in harvested energy and consumption, we analyze on-off (OO) jamming and always-on (AO) jamming schemes. The analytical expressions are obtained for secrecy outage probability (SOP). This analysis models the energy arrival and departure process by a discrete-time continuous-state Markov chain to eliminate the computational complexity and inaccuracy of a discrete-state Markov chain. Both the schemes are compared using SOP and secure throughput. This analysis shows the adequacy of a finite buffer for an EH jammer and also the fact that the availability of jamming power has a more pronounced effect on SOP as compared to a larger number of antennas at the jammer.

Peak Age of Information in Priority Queuing Systems

We consider a priority queueing system where a single processor serves k classes of packets that are generated randomly following Poisson processes. Our objective is to compute the expected Peak Age of Information (PAoI) under various scenarios. In particular, we consider two situations where the buffer size at each queue is one and infinite, and in the infinite buffer size case we consider First Come First Serve (FCFS) and Last Come First Serve (LCFS) as service disciplines. For the system with buffer size one at each queue, we derive PAoI exactly for the case of exponential service time and bounds (which are excellent approximations) for the case of general service time, with small k. For the system with infinite buffer size, we provide closed-form expressions of PAoI for both FCFS and LCFS where service time is general and k could be large. Using those results we investigated the effect of ordering of priorities and service disciplines for the various scenarios. We perform extensive numerical studies to validate our results and develop insights.

On the Stochastic Analysis of a Quantum Entanglement Switch

We study a quantum entanglement switch that serves k users in a star topology. We model variants of the system using continuous-time Markov chains (CTMCs) and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can easily model the effects of decoherence of quantum states using this technique. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can significantly affect performance. We also learn that, in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

Performance Analysis of Turbo Codes and Distributed Turbo Codes in Buffer-Aided Relay Systems

In this paper, we investigate the performance of a relay selection scheme in a buffer-aided multi-relay network with coded transmissions. We consider: (1) two different coding schemes, i.e., Turbo codes and distributed Turbo codes (DTC) and (2) quasi-static Rayleigh fading channels, where all the links are independent but asymmetric. For each of the aforementioned schemes, we analyze the performance of the system in terms of the average throughput and average delay. In addition, simple and explicit approximations of the asymptotic throughput for infinite buffer size and the high signal-to-noise ratio (SNR) regime are obtained. Our analysis of the asymptotic throughput provides the maximum achievable diversity gain of the system, and the accuracy of the derived analytical framework is assessed when compared to the Monte-Carlo simulations.

Analysis of handoff delay for proactive spectrum handoff scheme with PRP M/G/1/K queuing system in cognitive radio networks

Spectrum handoff has a negative impact on the performance of cognitive users (CUs) in terms of handoff delay in cognitive radio (CR) networks. In this study, a pre-emptive resume priority (PRP) M/G/1/K queuing network model is proposed with a finite number of allowable interruptions for proactive decision spectrum handoff scheme in order to minimise the cumulative handoff delay (CHD) and total service time (TST) for CUs. The CHD and TST for different proactive decision handoff schemes: non-switching spectrum handoff, switching spectrum handoff, and random spectrum handoff are modeled under the proposed PRP M/G/1/K queuing network model. Comprehensive results of CHD and TST are obtained to compare the performances of the proactive decision handoff schemes under the proposed PRP M/G/1/K queuing network model. This study also presents an analytical framework to examine the effect of primary users activity and buffer size on spectrum handoff delay performance with a finite number of allowable interruptions in a CR network. Thereafter, the optimal buffer size (K) is estimated for the proposed PRP M/G/1/K queuing network model, which gives performance similar to the infinite buffer size PRP M/G/1 queuing model with negligible (<1%) error.

Wireless Security Employing Opportunistic Relays and an Adaptive Encoder Under Outdated CSI and Dual-Correlated Nakagami-&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$m$ &lt;/tex-math&gt; &lt;/inline-formula&gt; Fading

This paper gives a novel perspective on physical layer security (PLS) and end-to-end (e2e) analysis under dual correlated Nakagami-m fading, and outdated channel state information, by employing 1) decode-and-forward opportunistic relays, and 2) an adaptive encoder with ON/OFF transmission. Assuming an infinite relay buffer size, two new sets of independent results for 1) non-integer fading parameter m, mathematically employing infinite summations, and 2) integer m, mathematically employing finite summations, are obtained. The adaptive encoder deployment improves transmission quality, and simultaneously enhances secrecy performance. The proposed e2e analysis coherently links secrecy, and e2e system performance for the first time under dual correlated Nakagami-m fading. Findings for wireless secrecy, and e2e system analysis with the non-integer fading parameter m offer an extra dimension to existing PLS literature, which has chronically been valid for only integer m. Convergence for infinite summations is achieved for a finite number of terms, realising the practicality of the proposed findings. Monte Carlo simulation successfully validates the new findings for non-integer m, and an asymptotic analysis under several specific scenarios is also presented.

Secrecy and End-to-End Analyses Employing Opportunistic Relays Under Outdated Channel State Information and Dual Correlated Rayleigh Fading

Exact secrecy and end-to-end (e2e) system analyses for cooperative wireless networks employing a best-relay-selection method with imperfect or outdated channel state information, an infinite relay buffer size, and a wire-tap channel under dual correlated Rayleigh fading are given. The new findings, which are valid for any value of the combined signal-to-noise ratio, generalize existing findings in the literature. Closed-form expressions for probability density function, cumulative distribution function, moment generating function, outage probability under secrecy, and e2e system performance are given using one- and two-dimensional Laplace transform. Secrecy outage probability employing an adaptive encoder is also derived, which coherently links secrecy performance and e2e system performance under dual correlated Rayleigh fading for the first time. Effects of amount of fading on secrecy are discussed. Simulation results are shown to match theoretical predictions. Detailed discussions and insight are also given.

Reliability with finite buffer size for a multistate manufacturing system with parallel production lines

This study examines system reliability for a manufacturing system with parallel production lines by creating a model of a multistate manufacturing system (MMS). System reliability is defined as the probability of demand satisfaction, which reflects the probability that the current capacity state of the MMS can successfully process a given demand. In particular, a buffer station with a finite size is taken into consideration to avoid blockage and starvation in the MMS. To the best of our knowledge, there is no existing research that considers a finite buffer size in a model of an MMS with parallel production lines. This study proceeds through the following phases. (i) In the model construction phase, the amount of input material, workload, and minimal capacity required by each workstation to satisfy a given demand level are studied by flow analysis; subsequently, a buffer usage matrix (BUM) is proposed to calculate buffer reliability. (ii) In the performance evaluation phase, system reliabilities with both infinite and finite buffer sizes are derived in terms of both minimal capacity vector and buffer reliability. (iii) In the case demonstration phase, two examples are utilized to illustrate the proposed method. Results of both examples show that the system reliability is overestimated with an infinite buffer size.

Analysis of an optimal stopping problem for software rejuvenation in a deteriorating job processing system

Software rejuvenation is the proactive maintenance operation for software systems that experience software aging causing degradations in system performance and reliability. The normal system performance can be recovered by software rejuvenation, which restarts the software system to clear all the internal error states due to software aging. Since software rejuvenation drops all the jobs in the system, a trigger for software rejuvenation needs to be carefully determined in consideration of such costs. In this paper, we theoretically derive the optimal policy that minimizes the cost of decision for software rejuvenation in a deteriorating job processing system, which is modeled as an M/M/1 queue with infinite buffer size. In our model, the number of queued jobs is used to represent the system state and the decision of rejuvenation is made upon the completion of a foreground job. We formulate the problem as an optimal stopping problem to analytically derive the optimal policy for the rejuvenation decision. The analytical results show that the optimal stopping policy is determined by the service degradation rate, the costs of dropped jobs and delayed jobs, and it does not depend on the number of queued jobs. This indicates that whether to trigger rejuvenation can be decided immediately when the system confirms the level of service degradation, regardless of the number of queued jobs at that time instant.

Packet Drop Probability Analysis of Dual Energy Harvesting Links With Retransmission

In this paper, we consider point-to-point dual energy harvesting (EH) links, where both transmitter and receiver are EH nodes (EHNs), with a retransmission protocol: either an automatic repeat request (ARQ) or hybrid ARQ with chase combining. We develop a framework to analyze the impact of various physical layer parameters, e.g., the energy harvesting profiles, size of energy buffer, and power management policies , at both the transmitter and receiver, and the channel statistics and coherence time , on the packet drop probability (PDP) of dual EH links over block fading channels. We derive the closed-form expressions for the PDP of a retransmission index-based power management policy. The presented framework naturally extends to obtain the PDP of mono EH links, i.e., links where only one of the two nodes harvests energy. To obtain further insights, we analyze the PDP of links with zero and infinite energy buffer size, and characterize the energy unconstrained regime , where the PDP is governed only by the average harvesting rate. Through extensive Monte Carlo simulations, we demonstrate the accuracy of the theoretical expressions, compare performance against existing power management schemes, and illustrate the performance tradeoffs involved.

Buffer-Aided Relaying With Outdated CSI

Adaptive link selection for buffer–aided relaying can provide significant performance gains compared to conventional relaying with fixed transmission schedule, when perfect channel state information (CSI) is available for link selection. However, in practice, link selection may have to be performed based on outdated CSI, because of infrequent feedback of CSI and/or feedback delay. In this paper, we study the effect of outdated CSI on the error rate performance of adaptive link selection for a three node decode–and–forward (DF) relay network with fixed–rate transmission. In particular, we propose two protocols for link selection based on whether the reliability of the CSI estimates is known or not. For both protocols, we provide a unified error-rate analysis in terms of a decision threshold $\beta$ , which can be adjusted to maintain buffer stability, and derive asymptotic approximations, which reveal the diversity and coding gains. Since packet transmission delay is unavoidable for opportunistic link selection, we analyze the average delay and throughput considering both finite and infinite buffer size. The average delay and throughput are functions of the decision threshold $\beta$ , which can be optimized to minimize the error rate while satisfying average delay and/or throughput constraints. Numerical results manifest that even with outdated CSI, adaptive link selection provides a significant coding gain advantage over conventional DF relaying. Furthermore, we show that a diversity gain of two can be achieved for perfect CSI and the optimum error rate can be approached with small delay and/or high throughput.

State-dependent M/G/1 queueing systems

We consider a state-dependent $$M_{n}$$Mn/$$G_{n}$$Gn/1 queueing system with both finite and infinite buffer sizes. We allow the arrival rate of customers to depend on the number of people in the system. Service times are also state dependent and service rates can be modified at both arrivals and departures of customers. We show that the steady-state solution of this system at arbitrary times can be derived using the supplementary variable method, and that the system's state at arrival epochs can be analyzed using an embedded Markov chain. For the system with infinite buffer size, we first obtain an expression for the steady-state distribution of the number of customers in the system at both arbitrary and arrival times. Then, we derive the average service time of a customer observed at both arbitrary times and arrival epochs. We show that our state-dependent queueing system is equivalent to a Markovian birth-and-death process. This equivalency demonstrates our main insight that the $$M_{n}$$Mn/$$G_{n}$$Gn/1 system can be decomposed at any given state as a Markovian queue. Thus, many of the existing results for systems modeled as an M / M / 1 queue can be carried through to the much more practical M / G / 1 model with state-dependent arrival and service rates. Then, we extend the results to the $$M_{n}$$Mn/$$G_{n}$$Gn/1 queueing systems with finite buffer size.

Efficient Methods to find the Equilibrium Distribution of the Number of Customers in GI/M/c Queues

In this paper, we review some of the methods used to find the number of customers in system in an GI/M/c/N queue for finite and infinite buffer sizes N, and we add some new methods. It was found that with modern computers, most of these methods provide results in a fraction of a second, even for high values of c and N. We also show that the traditional methods for dealing with infinite buffers lead to double integrals, a problem that is avoided by using a novel method we suggest.

Diversity and Delay Analysis of Buffer-Aided BICM-OFDM Relaying

In this paper, we study a cooperative diversity scheme for wireless systems where the relay is equipped with a buffer. We consider practical frequency—selective channels and adopt the combination of bit interleaved coded modulation and orthogonal frequency division multiplexing (BICM—OFDM). We propose a novel link selection protocol for BICM—OFDM systems where the relay either transmits or receives in a given time slot depending on the quality of the links. We derive a closed—form upper bound for the asymptotic worst—case pairwise error probability (PEP) and the diversity gain of the considered buffer—aided relaying scheme for both infinite and finite buffer size. We show that significant diversity gains can be achieved with buffer—aided relaying compared to conventional relaying at the expense of larger packet delays. In fact, for buffers of infinite (or very large) size, the diversity gain is doubled for links with identical frequency diversity, and an even higher diversity gain advantage is possible for links with non—identical frequency diversities. Furthermore, we perform an exact closed—form average delay analysis for buffers of both finite and infinite size which provides important insight into the achieved delay—performance tradeoff. The derived analytical results and performance gains are corroborated by extensive simulation results.

Mean station reliabilities cause throughput overestimates in production system design

In production system design, we typically lack actual station reliability data for throughput analysis using a model, because these stations do not yet exist. Hence, we either use the mean values from similar existing equipment or mean reliability estimates provided by equipment manufacturers. The real stations may have better or worse reliabilities compared to the means. Hence, when the system is built, the real system throughput may be acceptable or poor depending on actual station reliabilities. This paper compares predicted model throughput using station mean reliabilities with real system throughput. We find that the model often overestimates system throughput. We develop an upper bound and the maximum probability of overestimation when there is an infinite buffer size after each station. We also provide the ranges of overestimation for systems with limited buffers. These results may be used as a “rule of thumb” to adjust system throughput estimation. Monte Carlo simulation is discussed as an approach to analyze real system performance.

Approximation methods for the analysis of a multicomponent, multiproduct assemble-to-order system

In this article, we consider the performance evaluation of a multicomponent, multiproduct assemble-to-order (ATO) system. Each component is managed independently using a base-stock policy at a supply facility with limited production capacity and an infinite buffer. The arrivals of demands follow a multivariate Poisson process and unfilled demands are backlogged. Because exact analysis of the proposed system is not feasible, we propose two approximation methods which provide upper and lower bounds for various performance measures such as fill rate, average waiting time, and average number of backorders of the proposed system. Our computational experiments demonstrate the effectiveness of the two approximation methods under various system settings. In this article, we consider an assemble-to-order (ATO) system in which multiple components are produced to meet demands of multiple products. Each component supply facil- ity has limited production capacity with i.i.d. exponential processing time; its inventory is replenished using a base- stock policy; and the replenishment orders for the component are placed in a queue with an infinite buffer size. The arrivals of demands follow a multivariate Poisson process, in which an arriving order of a certain product will request a num- ber of components with a fixed probability. The demand orders are filled on first-come-first-serve basis and unfilled orders, due to shortage of one or more components, will be backlogged. Throughout this article, we will call the above- described system the infinite buffer ATO system, or IBS in short. We are interested in the analysis of three order-based per- formance measures of the IBS, namely, average waiting time of an order, the average number of backorders, and

Algorithm for waiting time distribution of a discrete-time multiserver queue with deterministic service times and multi-threshold service policy

In this paper, a discrete-time multiserver queueing system with infinite buffer size is studied. Packets arrive at the system according to a Bernoulli arrival process, and the service times of the packets are assumed to be constant equal to an integer multiple of slots. The number of active servers in the system is controlled by a so-called multi-threshold service policy with a set of thresholds predefined. For this multiserver system, we derive its stationary waiting time distribution by using the stochastic complement and Crommelin's techniques. We also present an algorithm for computing the stationary waiting time distribution.

Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic

We address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on the current state of the system. An infinite horizon cost minimization problem is considered here. The cost function includes a penalty for each rejected customer, a control cost related to the adjustment of the service rate and a penalty for each abandoning customer. We obtain an explicit optimal strategy for the limiting diffusion control problem (the Brownian control problem or BCP) which consists of a threshold-type optimal rejection process and a feedback-type optimal drift control. This solution is then used to construct an asymptotically optimal control policy, i.e. an optimal buffer size and an optimal service rate for the queueing system in heavy traffic. The properties of generalized regulator maps and weak convergence techniques are employed to prove the asymptotic optimality of this policy. In addition, we identify the parameter regimes where the infinite buffer size is optimal.