Blocking Probability Research Articles

Routing Algorithms for SDM Flexible Optical Networks

This paper considers the online routing, modulation, spectrum, and core allocation problem in elastic optical networks. Three algorithms are proposed to minimize the bandwidth blocking probability while taking into account the impact of interference from established lightpaths. These algorithms are based on a sequence of alternative paths, ordered in terms of increasing lengths, determined by Yen’s algorithm. Each of the algorithms for the selected single or dual lightpath enforces the constraints of spectrum continuity, contiguity of the slots, and non-overlapping of the spectra with the established lightpaths, maximizes the number of bits per symbol, and selects a specific core on each link of the path. Simulation studies performed for two sample networks showed that the crosstalk has a significant impact on the bandwidth blocking probability. The best results were obtained by iterating over all paths and all slots, selecting the lightpath with the lowest average crosstalk per slot, consisting of the most loaded cores.

Optical circuit switched three-stage twisted-folded Clos-network design model guaranteeing admissible blocking probability

Some data center networks have already started to use optical circuit switching (OCS) with potential performance benefits, including high capacity, low latency, and energy efficiency. This paper addresses a switching network design to maximize the network radix, i.e., the number of terminals connected to the network under the condition that a specified number of identical switches with the size N×N and the maximum admissible blocking probability are given. Previous work presented a two-stage twisted and folded Clos network (TF-Clos) with a blocking probability guarantee for OCS, which has a larger network radix than TF-Clos with a strict-sense non-blocking condition. Expanding the number of stages allows for enhancing the network radix. This paper proposes a model designing an OCS three-stage TF-Clos structure with a blocking probability guarantee to increase the network radix compared to the two-stage TF-Clos. We formulate the problem of obtaining the network configuration that maximizes the network radix as an optimization problem. We conduct an algorithm based on an exhaustive search to obtain a feasible solution satisfying the constraints of the optimization problem. This algorithm identifies the structure with the largest network radix in non-increasing order to avoid unnecessary searches. Numerical results show that the proposed model achieves a larger network radix than the two-stage model.

Resource learning aware algorithm for route prediction and resources allocation in elastic optical networks with network analytics

We have proposed two algorithms in this paper for dynamic traffic in elastic optical networks (EON). Algorithm1 considers the spatial access blocking probability metric (SABPM) during dynamic operation and route traffic to a path with lower SABPM. Therefore, it considers a path with more contiguous blocks to support heterogeneous bandwidths (BW) and modulation schemes. Algorithm1 keeps a balance of fragmentation on available routes. Algorithm2 makes routing decision for dynamic traffic based on the maximum idle slots as well as minimum SABPM. Therefore, it selects a less fragmented path with more number of available contiguous blocks to support heterogeneous BW. Algorithm2 balances the path utilization and avoids over utilization of congested route. We have evaluated the performance of both algorithms in terms of spatial external fragmentation, contiguity ratio, contiguous aligned spectrum ratio, SABPM, and BW blocking probability (BwBP). Python with seaborn, pandas, and other libraries are used for network analytics. Results show that resource utilization improves with the proposed algorithms. It has been shown that algorithm2 and algorithm1 achieve 27% and 18% traffic gains respectively over the alternate routing.

Dynamic capacity sharing with multi-wavelength integrated transmitters in hybrid datacenter networks

In datacenters, bursty and unevenly distributed traffic may lead to serious network performance degradation. Various methods, including reconfigurable optical circuit switching (OCS), traffic control techniques, valiant load balancing (VLB), and so on, have been proposed to solve this problem. Based on these solutions, our method makes a trade-off between cost and performance. In this paper, we propose to use multi-wavelength tunable transmitters in our previously proposed modular arrayed waveguide grating (AWG)-based interconnection network. We discuss how the multiple wavelengths can be shared in the network and then propose a computational model to study its blocking probability. Closed-form equations for low network load cases are also derived to provide the analytical expression for the blocking probability. We verify the accuracy of our computational model through simulations. Comparing the blocking probability of networks with and without multi-wavelength integrated transmitters, we show that network performance can be considerably improved after replacement. When traffic burstiness is 1.25 and traffic skewness is 0.08, the blocking probability is reduced from 0.14 to 3.60×10−3 after replacing in each sending module one fixed laser with multi-wavelength tunable transmitters with four wavelengths. Furthermore, we also discuss how different factors influence the blocking probability and the maximum load with the given network performance requirement.

Physical layer-aware circuit reallocation to eons using make-before-break and push-pull techniques

This paper proposes a new circuit reallocation algorithm with make-before-break and push-pull techniques that considers the effects of physical layers in transparent elastic optical networks called Just One Circuit Reallocation (JOC). The JOC algorithm reallocates just one already established circuit to avoid blocking new circuit requests due to impairments in the physical layer. The results of the JOC algorithm were compared to three other algorithms: Circuit Reallocation Strategy - Physical Layer (CRS-PL), Circuit Reallocation for Block Reduction related to the QoT of the circuits (R-RQoT), and Make-Before- Break based defragmentation algorithm (MBBr). The reallocation algorithms are evaluated under the Bandwidth Blocking Probability (BBP), Circuit Blocking Probability (CBP), and the Number of reallocated circuits (N), external fragmentation, and percerntual of circuit by modulation for USA and EON topologies. Moreover, we also evaluated the performance of reallocation algorithms using complete sharing, K-shortest path computation, modified Dijkstra paths computation, and K-shortest path with reduction of QoTO to routing and spectrum assignment. Simulation results show that the proposed algorithm performs better than the CRS-PL, R-RQoT and MBBr algorithms regarding BBP, PBC, and N. Regarding BBP our algorithm presented minimum reductions of approximately 65.36% e 55.6% for the USA and EON topology, respectively.

A study of a loss system with priorities

The Erlang loss formula, also known as the Erlang B formula, has been known for over a century and has been used in a wide range of applications, from telephony to hospital intensive care unit management. It provides the blocking probability of arriving customers to a loss system involving a finite number of servers without a waiting room. Because of the need to introduce priorities in many services, an extension of the Erlang B formula to the case of a loss system with preemptive priority is valuable and essential. This paper analytically establishes the consistency between the global balance (steady state) equations for a loss system with preemptive priorities and a known result obtained using traffic loss arguments for the same problem. This paper, for the first time, derives this known result directly from the global balance equations based on the relevant multidimensional Markov chain. The paper also addresses the question of whether or not the well-known insensitivity property of the Erlang loss system is also applicable to the case of a loss system with preemptive priorities, provides explanations, and demonstrates through simulations that, except for the blocking probability of the highest priority customers, the blocking probabilities of the other customers are sensitive to the service time distributions and that a larger service time variance leads to a lower blocking probability of the lower priority traffic.

Deep-reinforcement-learning-based RMSCA for space division multiplexing networks with multi-core fibers [Invited Tutorial

The escalating demands for network capacities catalyze the adoption of space division multiplexing (SDM) technologies. With continuous advances in multi-core fiber (MCF) fabrication, MCF-based SDM networks are positioned as a viable and promising solution to achieve higher transmission capacities in multi-dimensional optical networks. However, with the extensive network resources offered by MCF-based SDM networks comes the challenge of traditional routing, modulation, spectrum, and core allocation (RMSCA) methods to achieve appropriate performance. This paper proposes an RMSCA approach based on deep reinforcement learning (DRL) for MCF-based elastic optical networks (MCF-EONs). Within the solution, a novel state representation with essential network information and a fragmentation-aware reward function were designed to direct the agent in learning effective RMSCA policies. Additionally, we adopted a proximal policy optimization algorithm featuring an action mask to enhance the sampling efficiency of the DRL agent and speed up the training process. The performance of the proposed algorithm was evaluated with two different network topologies with varying traffic loads and fibers with different numbers of cores. The results confirmed that the proposed algorithm outperforms the heuristics and the state-of-the-art DRL-based RMSCA algorithm in reducing the service blocking probability by around 83% and 51%, respectively. Moreover, the proposed algorithm can be applied to networks with and without core switching capability and has an inference complexity compatible with real-world deployment requirements.

Use of machine learning and Poincaré density grid in the diagnosis of sinus node dysfunction caused by sinoatrial conduction block in dogs.

Sinus node dysfunction because of abnormal impulse generation or sinoatrial conduction block causes bradycardia that can be difficult to differentiate from high parasympathetic/low sympathetic modulation (HP/LSM). Beat-to-beat relationships of sinus node dysfunction are quantifiably distinguishable by Poincaré plots, machine learning, and 3-dimensional density grid analysis. Moreover, computer modeling establishes sinoatrial conduction block as a mechanism. Three groups of dogs were studied with a diagnosis of: (1) balanced autonomic modulation (n = 26), (2) HP/LSM (n = 26), and (3) sinus node dysfunction (n = 21). Heart rate parameters and Poincaré plot data were determined [median (25%-75%)]. Recordings were randomly assigned to training or testing. Supervised machine learning of the training data was evaluated with the testing data. The computer model included impulse rate, exit block probability, and HP/LSM. Confusion matrices illustrated the effectiveness in diagnosing by both machine learning and Poincaré density grid. Sinus pauses >2 s differentiated (P < .0001) HP/LSM (2340; 583-3947 s) from sinus node dysfunction (8503; 7078-10 050 s), but average heart rate did not. The shortest linear intervals were longer with sinus node dysfunction (315; 278-323 ms) vs HP/LSM (260; 251-292 ms; P = .008), but the longest linear intervals were shorter with sinus node dysfunction (620; 565-698 ms) vs HP/LSM (843; 799-888 ms; P < .0001). Number and duration of pauses, not heart rate, differentiated sinus node dysfunction from HP/LSM. Machine learning and Poincaré density grid can accurately identify sinus node dysfunction. Computer modeling supports sinoatrial conduction block as a mechanism of sinus node dysfunction.

Stochastic Models of Traffic Management

This article discusses the problem of blocking nodes in road networks and percolation thresholds for the transport infrastructure of a modern metropolis. For metropolitan networks, the values of percolation thresholds are calculated and displayed, considering the different density of connections between network nodes. Further, it is shown that the dependence of the values of the percolation thresholds on the network’s density can be described by functional dependencies with a high degree of correlation. The obtained results can be used to assess the reliability of transport infrastructure and to check the increase in the capacity of selected sections of the road network. Further, the article discusses obtaining a description of road infrastructure from open sources (obtaining data from OpenStreetMap using the SUMO - Simulation of Urban MObility package), after which it is possible to build a graph of the road network and determine its percolation properties. For the constructed nodes of the graph described a model of the stochastic dynamics of blocking a single road lane in the transport network. The threshold value L of number of cars that can be placed in the lane (based on the length of the road lane) is used as constraints and the incoming and outgoing flows of cars are also determined as income parameters of a model. The constructed model allows us to obtain the predicted blocking time of a road network line, for a given probability of such blocking, where the probability of blocking a single road network line is taken from the percolation properties of this network discussed earlier. The resulting blocking times of road network nodes make it possible to build an algorithm for controlling traffic light regulation.

Erlang-U: Blocking Probability of UAV-Assisted Cellular Systems

In modern and future communication systems, we expect peaks of traffic that largely exceed the capacity of the system, since they are originally designed to support normal traffic loads. Such peaks can be caused by emergency events and cultural or sporting gatherings, among others. Indeed, implementing more channels than the ones required in normal traffic conditions would entail higher costs and energy consumption. As such, when a traffic peak arrives, the system performance is greatly affected. To this end, we propose the use of mobile channels that assist cellular systems to increase the capacity of the network for a certain period. In this paper, we derive the blocking probability of a UAV (Unmanned Aerial Vehicle)-assisted cellular system to temporarily increase the capacity of the communication network in case of a traffic overload. The analysis presented in this work allows a careful design of future communication systems requiring fewer channels, that can serve users in normal traffic load conditions while using UAVs to maintain an adequate blocking probability when the traffic load increases. To this end, we develop the ErlangU formula, similar to the ErlangB formula for a conventional voice service cellular system.

Applying Fast Simulation to the Evaluation of Customer Blocking Probability in the Multichannel Queuing System with Multicast Access

Applying Fast Simulation to the Evaluation of Customer Blocking Probability in the Multichannel Queuing System with Multicast Access

Twisted and Folded Clos-Network Design Model With Two-Step Blocking Probability Guarantee

Twisted and Folded Clos-Network Design Model With Two-Step Blocking Probability Guarantee

AnalyticalBP: Analytical Model for Blocking Probabilities Considering Crosstalk-Avoided Approach in Spectrally-Spatially Elastic Optical Networks

AnalyticalBP: Analytical Model for Blocking Probabilities Considering Crosstalk-Avoided Approach in Spectrally-Spatially Elastic Optical Networks

Design model of a twisted and folded Clos network with multi-step grouped intermediate switches guaranteeing admissible blocking probability

A future data center network is expected to be constructed by a Clos network consisting of optical-circuit switches to deal with traffic growth. A previous model addressed a Clos-network design problem that divides the set of intermediate switches by each role for request routing to guarantee an admissible blocking probability to maximize the switching capacity. However, the previous model divides the set of intermediate switches into at most only two groups, and there is room for a more flexible design by increasing the number of divisions. This paper proposes a design model that generalizes the number of divisions to increase the switching capacity while guaranteeing an admissible blocking probability. We formulate the design model as an optimization problem. We introduce two algorithms to obtain a feasible solution that satisfies the constraints of the optimization problem. Numerical results showed that the proposed model can increase the switching capacity as the number of divisions increases.

Estimation Algorithm to Improve Cellular System Performance by Moving Base Stations locations

Cellular system adopts the idea of frequency reuse, where the frequency bandwidth of each cell is repeated in non-adjacent cell, in order to use the available frequency band efficiently, however, the interference occurs even between the distant cells. The aim of the paper is to reduce the interference between these co-cells.The user receives the signal from its own cell, as well as the signal from the far cell which has the same frequency, the parameter Signal to Interference Ration, SIR, is the main factor to evaluate the performance of the cellular system.In this paper, we propose algorithm to move the locations of base stations of the cells, in order to increase SIR value, decrease Probability of blocking, and number of users out of coverage.

Optimizing performance in elastic optical networks using advanced reconfigurable optical add-drop multiplexers: A novel design approach and comprehensive analysis

Network operators diversify service offerings and enhance network efficiency by leveraging bandwidth-variable transceivers and colorless flexible-grid reconfigurable optical add-drop multiplexers (ROADMs). Nonetheless, the paradigm shift from rigid to elastic optical networks (EONs) has affected several key parameters, including bit rate, center frequency spacing, modulation format, and optical reach. This study investigated the transformative impact of emerging technologies on the design and structure of optical network architectures, including spectrally efficient multicarrier systems and bandwidth-variable wavelength-selective switches. A cost-effective ROADM architecture applying an order-based connecting approach was introduced, which presented a high connectivity level and a blockage probability of less than 10-4. When this architecture was implemented in the EON, the data transportation rate was 1 Tb/s. This outcome successfully accommodated a 20 % surge in traffic demand, while the optimized network architecture significantly improved fiber utilization by 3.4 %. Consequently, this study contributed a practical and efficient solution for implementing flexible optical networks, effectively addressing current concerns and propelling the optical communication system sector forward.

Routing and dynamic core allocation with fragmentation optimization in EON-SDM

The increasing need for rapid data transmission in optical networks has made the effective allocation of spectrum resources a crucial necessity. This study presents a new spectrum allocation approach that incorporates path selection and careful consideration of cross-talk (XT) limitations. We propose a novel fragmentation coefficient and dynamic core-changing-based routing, spectrum, and core allocation (FC-DCC-RSCA) technique. The algorithm begins by searching for the shortest paths using the Dijkstra algorithm. It then proceeds to evaluate fragmentation coefficients (FC) using the Continuous Aligned Slot Ratio (CASR) model. Subsequently, the FC undergoes a filtration process wherein only those falling inside predetermined fragmentation ranges (min and maxFC) are retained. Further spectrum allocation has been done based on XT constraints. The algorithm has better proficiency in dynamic flexibility, enabling it to effectively handle varying traffic loads. By conducting a series of rigorous simulations, our proposed approach exhibits a notable decrease in bandwidth blocking probability (BBP) while also opening the door for considerable improvements in spectrum utilization. The algorithm’s proficiency in adapting to changing network circumstances signifies its importance as a helpful thing in enhancing the allocation of resources within optical networks. It is well-positioned to address the developing requirements of contemporary communication systems. The spectrum utilization of the FC-DCC-RSCA increases by 12.5% and 6.25%, exhibits a reduction in its FR by 13.5% and 2.7%, and has a BBP of 0.051 for the traffic load of 450 Erlang, compared to SBP-PMC and FMDE-RSCA. The algorithm that has been provided provides opportunities for more investigation and enhancement. Potential areas for future research include the examination of strategies to improve energy efficiency, the development of scalable solutions for bigger network infrastructures, and the incorporation of machine learning methodologies to facilitate dynamic decision-making processes. Furthermore, it is worth investigating the potential of the method to be applied in developing optical communication technologies, such as space-division multiplexing. These endeavors hold the potential to enhance the current level of knowledge and practices in the field of optical network management and optimization.

Computationally Efficient UE Blocking Probability Model for GBR Services in Beyond 5G RAN

Computationally Efficient UE Blocking Probability Model for GBR Services in Beyond 5G RAN

Integrating teletraffic theory with neural networks for quality-of-service evaluation in mobile networks

In mobile cellular design, one important quality-of-service metric is the blocking probability. Using computer simulation for studying blocking probability is quite time-consuming, whereas existing teletraffic-based methods such as the Information Exchange Surrogate Approximation (IESA) only give a rough estimate of blocking probability. Another common approach, direct blocking probability evaluation using neural networks (NN), performs poorly when extrapolating to network conditions outside of the training set. This paper addresses the shortcomings of existing teletraffic and NN-based approaches by combining both approaches, creating what we call IESA-NN. In IESA-NN, an NN is used to estimate a tuning parameter, which is in turn used to estimate the blocking probability via a modified IESA approach. In other words, the teletraffic approach IESA still forms the core of IESA-NN, with NN techniques used to improve the accuracy of the approach via the tuning parameter. Simulation results show that IESA-NN performs better than previous approaches based on NN or teletraffic theory alone. In particular, even when the NN cannot produce a good value for the tuning parameter, for example when extrapolating to network conditions not experienced in the training set, the final IESA-NN estimate is generally still accurate as the estimate is primarily determined by the underlying teletraffic theory, with the NN determining the tuning parameter playing a supplementary role. The combination of the IESA framework with NN in a secondary role makes IESA-NN quite robust.

Multi-Wavelength Path Loss Model for Indoor VLC with Mobile Human Blockage

Visible light communication (VLC) is one of the candidate technologies for the sixth generation (6G) networks. The path loss model is particularly important for link budget estimation and network planning in VLC. Due to the wideband nature and the extremely poor diffraction capacity of light, the path loss of the VLC channel is susceptible to wavelength dependence and blockage effect. In this paper, we propose a novel path loss model which can characterize the impact of wavelength dependence combined with mobile human blockage for both the single-LED (light emitting diode) and the multi-LED scenario. When there is no blockage in the channel, the multi-wavelength path loss under free space propagation is modeled with a small standard deviation of 0.262 in the single-LED scenario and a small root mean square error of 0.009 in the multi-LED scenario which indicates the high accuracy of the model. When considering the mobile human blockage, the blockage probability (BP) is modeled with full consideration of realistic human mobility and human body shadowing. The results indicate that the BP in single-LED scenario can reach 0.08, while the BP in multi-LED scenario is 0.022. This demonstrates that the distributed deployment of transmitters can effectively reduce the occurrence of the blockage state in VLC.