The current paper provides a cutting-edge information data length- theoretic approach to the transient M/M/Infinity queueing system. This is a first time ever investigation that unifies information data length and queueing theories. The significant impact of both time and the number of states for the transient M/M/ Infinity queue on both the upper and lower bounds of the obtained information data length is observed and noted. The paper concludes with some challenging open problems, combined with concluding remarks and future research pathways.

This paper provides an overview of modelling and simulation methods for complex systems, including queuing and life support systems. To realize and capture every aspect of a system or situation, a model is used in place of the actual one. Using a model and simulation, we may create scenarios and make decisions. Computer experiments with the model can save costs, time, and effort once its validity has been shown. A model of the thing under study is created by computer simulation, which then runs the model on a digital computer and examines the results. It's interesting to note that a knowledge base of data includes information about predicted behaviour of the model as well as coordinated determination of external variables and parameters. Selecting the precise model creation technique is the first and most difficult task in simulation. A review of techniques used in simulation model execution (serial and parallel discrete-event simulation), simulation model analysis (calibration, validation, verification, goal-seeking), and conceptual, declarative, functional, constraint, and multimodal design are presented in this paper.

We study the robustness of the cμ-rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FCFS retrial discipline, when the customers at the head of queues repeatedly tries to occupy the server in a random time. It is proved that for the scheduling problem in the system without arrivals the cμ-rule minimizes the total average cost. For the system with arrivals it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes for the certain values of system parameters the service exclusively for the class-i customers if both of queues are not empty with the aim to minimize the average cost per unit of time. It is also shown that in a finite-buffer case the cμ-rule fails.

The problem of blood delivery has been a critical concern in past decades. However, the unsteady behavior of blood donors, along with the uncertainties associated with demands in a crisis imposes several challenges for resource management. In this research work, we analyze the blood delivery behavior in a crisis modeled by coupled queues of patients and blood sources. Using Markovian modeling and results associated with G-network, we derive two critical probabilities, namely lack of unit of blood (unit of donations) or not having any storage capacity left to accept new donors' blood. We propose a closed-form solution to calculate the optimal blood storage size, and also we suggest sufficient conditions that guarantee the feasibility of the model. Finally, we conduct a sensitivity analysis to investigate the impact of model parameters on storage size and the proportion of time that storage is full.

Although the dockless bike-sharing system, which can be regarded as a typical example of the resource-sharing system, has been increasingly popular for years with people especially in China, the imbalanced distribution of shared bikes gradually becomes a major problem for both bike-sharing companies and their customers. To solve the imbalance problem, we aim to investigate the long-term performance of a system under the influence of some key factors (with an emphasis on the unequal demand between different nodes), which can guide us to discover the causes of the problem and offer several valuable suggestions to the operators. According to the fundamental principle of a dockless bike-sharing system, we propose a model reduction method to reduce the complexity of the theoretical network models, which are developed based on the Markovian queueing theory with the consideration of higher-demand nodes and lower-demand nodes. The theoretical network models provide us with steady-state probabilities of having a certain number of bikes at one node, which are used as an important part of the optimization model for solving the imbalance problem by carrying out an operator-based relocation strategy. The objective of the optimization model is to maximize the total profit and determine the optimal relocation frequency. It is found that most of the shared bikes are possible to gather at one low-demand node eventually in the long run under the influence of the different arrival rates at different nodes, but the decrease of the number of bikes at the high-demand nodes is more sensitive to the unequal demands and may cause a great loss for operators, which should be payed attention to especially when solving the relocation problems.

This paper investigates the search for an exact analytic solution to a temporal first-order differential equation that represents the number of customers in a non-stationary or time-varying

Complex dynamical fluctuations, from molecular noise within cells, collective intelligence, brain dynamics or computer traffic have been shown to display noisy behaviour consistent with a critical state between order and disorder. Living close to the critical point can have a number of adaptive advantages and it has been conjectured that evolution could select (and even tend to) these critical states. One way of approaching such state is by means of so-called self-organized criticality (SOC) where the system poises itself close to the critical point. Is this the case of living cells? It is difficult to test this idea given the enormous dimensionality associated with gene and metabolic webs. In this paper, we present an alternative approach: to engineer synthetic gene networks displaying SOC behaviour. This is achieved by exploiting the presence of a saturation (congestion) phenomenon of the ClpXP protein degradation machinery in E. coli cells. Using a feedback design that detects and then reduces ClpXP congestion, a {\em critical motif} is built from a two-gene network system, where SOC can be successfully implemented. Both deterministic and stochastic models are used, consistently supporting the presence of criticality in intracellular traffic. The potential implications for both cellular dynamics and designed intracellular noise are discussed.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.

The current work reports the upper bound of the state variable of the of the Pointwise Steady Fluid Flow Approximation (PSFFA) model of non-stationary M/Ek/1 queueing system.

Nowadays, wearable devices for human health monitoring are increasingly become popular and widely used. Typically, the wearable device is small size and operates with batteries. Therefore, the wearable device acquires bio-signals and transfers to smartphones or personal computers (PC) via WiFi/ Bluetooth for processing data. To reduce power consumption is one of the most important challenges of designing wearable devices. To solve this problem, the proposed signal quality valuation (SQV) method can be select the high-quality signal and reduce the transfer time to other devices. In this paper, the proposed SQV and data compression method rely on real-time PPG signals analysis to retain important information of PPG signal, improve performance and power consumption of PPG devices. Besides, we also proposed Heuristic rules for heart rate (HR) estimation with compression data. The experimental results show that the highest compression ratio (CR) is 387.8 with BIDMC Physionet database (sampling frequencies of 125 Hz) and HR error as 1.43 bpm for averaging absolute error (avAE), the standard deviation absolute error (sdAE as 0.4) and relative error mean (avRE as 0.019). The proposed real-time PPG measurement system (sampling frequency as 100/ 200/ 400 Hz) reduce power consumption and open the new structure for healthcare application systems

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.