Effective Arrival Rate Research Articles

Age-Optimized Multihop Information Update Mechanism on the LEO Satellite Constellation via Continuous Time-Varying Graphs

Low orbit satellite constellation as a relay network provides a possible solution for remote real-time data gathering applications, in which freshness information updates will be forwarded via dynamical intersatellite links (ISLs). Modeling by a time-varying network, this article studies minimizing Age of Information (AoI) of delivering the data through a multihop path, in particular, focusing on the effect of frequent interruptions of ISLs. Subjected to two constraints of path and effective arrival rate, the minimizing AoI problem is formulated to find a pair of optimal transmission delay and arrival rate. In particular, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -approximate optimal algorithm, called a latest update routing (LUR) algorithm, is proposed with a well-designed continuous time-varying graph. Using LUR, a set of paths can be obtained with degraded transmission delay that satisfies a given arrival rate. By screening all the arrival rates satisfying the effective constraint, the maximum rate and a corresponding path set that minimizes age can be found. The simulation results verified that a degraded average AoI can be obtained by the proposed path selection mechanism compared with the typical shortest delay path (SDP) strategy, minimum spanning tree (MST) strategy, and MAoIG. In particular, the numerical findings show that the proposed LUR reduces average AoI by a maximum of 12.66% compared with SDP, 75.28% compared with MST, and 69.3% compared with MAoIG, respectively, under different scenarios.

Signaling Service Quality Through Queue Disclosure

Problem definition: We consider a single-server queueing system where service quality is either high or low. The server, who knows its exact quality level, can signal this quality information to customers by revealing or concealing its queue length. Based on this queue disclosure action and the observed queue length in the case of a revealed queue, customers decide whether to join the system. Academic/practical relevance: The queue disclosure action is regarded as a signal indicating the service quality. Methodology: We develop a signaling game and adopt the sequential equilibrium concept to solve it. We further apply the perfect sequential equilibrium as an equilibrium-refinement criterion. Results: In our baseline model, where all of the customers are uninformed of service quality, the pure-strategy perfect sequential equilibrium is always a pooling one, except at several discrete values of market size (measured by the potential arrival rate). When the market size is below a certain threshold, both high- and low-quality servers adopt queue concealment; otherwise, both types of servers adopt queue revelation. We also consider a general scenario in which the market is composed of both quality informed and uninformed customers. Under this setting, when the server conceals the queue, we can fully characterize customers’ equilibrium queueing strategies and the corresponding effective arrival rates. The unique sequential equilibrium outcome is still a pooling one when the market size is either below a lower threshold or above an upper threshold. A separating equilibrium can occur only when the market size falls between two thresholds; under that circumstance, the uninformed customers can infer the server’s quality from its queue disclosure behavior. Managerial implications: Under separating sequential equilibria, uninformed customers can fully infer the quality information and thus behave in an informed way. Unlike studies where queue disclosure is not regarded as a quality signal, our study reveals that the signaling effect of queue disclosure increases (decreases) the effective arrival rate of the high-quality (low-quality) server and also increases the customers’ total utility when the server is of low quality. Funding: P. Guo acknowledges the financial support from the Research Grants Council of Hong Kong [Grant 15502820]. The research of M. Haviv was funded by Israel Science Foundation [Grant 1512/19]. Z. Luo acknowledges the financial support from the Internal Start-up Fund of the Hong Kong Polytechnic University [Grant P0039035] and the National Natural Science Foundation of China [Grant 71971184]. Y. Wang’s work was supported by the Research Grants Council of Hong Kong [Grant 15505019]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1170 .

On equilibrium threshold strategies when choosing between observable and unobservable queues

We consider threshold equilibrium strategies in a two-server memoryless queueing system where customers inspect one queue before deciding which queue to join. We show that such an equilibrium may not exist. A numerical study indicates that if threshold equilibria exist, the effective arrival rate to the unobserved queue is higher when the regime there is last-come first-served rather than first-come first-served.

Optimal queue length information disclosure when service quality is uncertain

We investigate a server's best queue disclosure strategy in a single‐server service system with an uncertain quality level (which is assumed to be binary). We consider this problem from the perspective of a Bayesian persuasion game. The server first commits to a possibly mixed strategy stating the probability that the queue length will be revealed to customers on their arrival given a realized quality level. The service quality level is then realized, and the server's corresponding queue‐disclosure action is observed by customers, who then update their beliefs regarding service quality and decide whether to join the service system. We reformulate the server's decision problem as looking for the best Bayes‐plausible distribution of posterior beliefs regarding service quality. We demonstrate that the maximal expected effective arrival rate, as a function of the prior belief, can be graphed as the upper envelope of all convex combinations of any two arbitrary points on the two effective arrival rate functions of the revealed and concealed queues. We show that when the market size is sufficiently small (large), the server always conceals (reveals) the queue, regardless of the realized service quality. Numerically, we find that in a medium‐sized market, the server's optimal commitment strategy is often hybrid or mixed, that is, randomizing queue concealment and revelation. We also extend our analysis to a situation in which the server aims to maximize social welfare. We show that under certain conditions, it is always beneficial for the welfare‐maximizing social planner to randomize queue concealment and revelation, regardless of the market size.

Data Transmission in SAGIN with FANET/MANET of Drones

The purpose of this article is to simulate data transmission and calculate traffic parameters in SAGIN air segment for which Ad Hoc network of flying drones is considered as a model. Traffic modeling is based on the manet-routing-compare example from the ns3 simulator library, which has been supplemented with code to calculate packet loss, throughput, and message transmission delays. The program allowed considering drones movement at both low and high speeds from 3.6 km/h to 72 km/h. The dependences of traffic losses on data transmission power, transaction sizes and data transmission speed are obtained and analyzed. The distribution of the average effective arrival rate λ and the throughput/goodput for drones has been studied. Comparing traffic characteristics in models with different numbers of drones allows to judge how the required quality of service can be achieved by choosing the right transmission parameters.

On the Rate and Age of Information for non-preemptive systems with prioritized arrivals and deterministic packet deadlines in IoT networks

In this paper, we consider two different classes of IoT sensors with high and low priorities in which both classes send their data to a Monitoring Center (MC) equipped with one server and a buffer to store the arrival packets waiting in the queue, representing an M/M/1/2 system. An error-free channel predominates the link between the sensors and MC. We assume a non-preemptive scheme applying priorities on the buffer in MC so that the packets with lower priority in the queue can be replaced by more urgent higher priority packets but not in the service, as well. The arrival packets are specified by deadline characteristic due to the great demand for fresh data. The deadline is provided to free the buffer and let the monitoring center be updated by the latest data. As significant parameters in calculating the throughput and freshness of data, Rate of Information (RoI) and system’s Age of Information (AoI) are investigated in the MC. Our goal is to study the effect of priority and packet deadlines on the rate and status update of the system. Thus, a Markov model is applied to derive the closed form expressions considering deterministic deadlines and the impact of high and low priority packets. Also, a new metric named the Age to Rate Ratio of Information (ARRoI) is introduced and discussed for better realization of the relation between effective arrival rate and AoI. Simulation results for various parameters confirm the analytical results and show that the newly introduced metric, ARRoI, could be employed in finding proper transmission rates.

Service segment competition: size or value, which matters?

We study a service market with two firms: one that provides regular and another that provides premium services. Customers are delay sensitive and heterogeneous in evaluating the service level. We study two competition games that differ in segmentation-marketing strategies. One is the size-based competition in which firms compete on the segment size dimension, and the other is the value-based competition in which firms compete on the segment target (regarding customer valuation) dimension. For both games, the Nash equilibrium always exists, and the (Pareto dominant) equilibrium is unique. Interestingly, the premium service provider's effective arrival rate can be increasing in its competitor's service rate in the value-based game. Moreover, we capture the conditions for the equilibrium market as either a monopoly or a duopoly and show that size-based competition helps sustain service variety. We also show that the prices are reduced in the value-based game; the premium (regular) service provider serves more (fewer) customers in the value-based game than in the size-based game. Our results show that value-based competition is more intensive in the sense that the number of customers who are served, customer surplus and social welfare are higher, while the total revenue of two firms is lower in the value-based competition than in the size-based competition.

Service Segment Competition with Strategic Customers: Size or Value, Which Matters?

We consider a service market with two firms that provide regular and premium services respectively. Customers are delay sensitive and heterogeneous on evaluating the service level. We show that the service differentiation, together with customer heterogeneity, results in market segmentation (based on customer self-selection). We then study two competition games that differ in segmentation-marketing strategies. One is the size-based competition, and the other is the value-based competition. For both games, the Nash equilibrium always exists, and the (Pareto dominating) equilibrium is unique. Interestingly, the premium service provider's effective arrival rate can be increasing in the firm's competitor's service rate in the value-based game. Moreover, we capture the condition for the equilibrium market as either a monopoly or a duopoly and show that size-based competition helps sustain the service variety. We also show that the prices are reduced in the value-based game; the premium (regular) service provider serves more (fewer) customers in the value-based game than in the size-based game. Numerical results illustrate that the number of customers who get served, the customer surplus and social welfare are higher, while the total revenue are lower in the value-based game than in the size-based game, thus indicating that the competition is more intensive in the value-based game than in the size-based game.

Optimization of Machine Repair System with Controlling Arrival and Switching Failure

Abstract This study investigates the machine repair problem involving a controlling arrival policy and standbys switching failure. The operation of controlling arrival policy is that when the number of customers reaches the maintenance facility’s capacity, no further arriving failed machines are allowed to enter the system until the system capacity decreases to a certain threshold value. We develop the steady-state solutions and some import system characteristics, such as the expected number of failed machines in the system, machine availability, the average switching failure rate, effective arrival rate, and expected waiting time in the system, etc. A cost model is developed to determine the optimal control policy at a minimum cost. A sensitivity analysis is also conducted to investigate the effect of changes in the system parameters on the expected cost function. Finally, we present some managerial insights through an application example.

A novel approach for designing rental vehicle repositioning strategies

An important tactical decision for vehicle rental providers is the design of a repositioning strategy to balance vehicle utilization with customer wait times due to vehicle unavailabilities. To address this problem, this article analyzes alternative repositioning strategies: a no-repositioning strategy, a customer repositioning strategy, and a vehicle repositioning strategy, using queuing network models that are able to handle stochastic demand and vehicle unavailabilities. Optimization models are formulated to determine the repositioning fractions for alternate strategies that minimize the rental provider’s cost by balancing repositioning costs with customer waiting penalty costs. The nonlinear optimization problems are challenging to solve because the objective functions are non-differentiable and the decision variables (such as effective arrival rates and customer repositioning fractions) are interrelated. Therefore, a two-phase sequential solution approach to estimate the repositioning fractions is developed. Phase 1 determines the effective arrival rates by developing an approximate network model, deriving structural results, determining a high-quality solution point, and refining the solution. Phase 2 determines the repositioning fractions by solving a transportation problem. Numerical experiments are used to evaluate the efficacy of the proposed solution approach, to analyze alternate repositioning strategies, and to illustrate how the developed techniques can be adopted to create a better readiness at a depot.

Economic application in a Bernoulli F-policy queueing system with server breakdown

For maintaining the service quality of working place, some kinds of arriving customers control policy are needed. This paper investigates a randomised arriving control policy of finite capacity queuing system with an unreliable server. In the investigated system, when the number of customers reaches the system’s capacity, further arriving customers are not allowed to enter the system. As the queue length decreases to a predefined threshold value, customers may either be allowed entering the system with an exponential startup time or the customers are still unable to enter the system. For such a system, we develop the steady-state solutions and some important system characteristics, such as the probability that the server is busy, effective arrival rate, expected waiting time in the system, etc. We also develop a cost model to determine the optimal control policy at a minimum cost. A sensitivity analysis is also conducted to investigate the effects of changes in the system parameters on the expected cost function. Finally, we present some managerial insights through an application example of the printed circuit boards manufacturing system.

A decomposition approach in network revenue management: Special case of hotel

In this article, we address the multiple-night stay hotel revenue management. Using a decomposition method, we transform the multiple-night stay revenue management into a single night. To this end, we define effective arrival rate for each night that is derived from all the booking requests that contain the night, excluding the possible ‘customer losses’. A customer is labeled ‘loss’ either because of the existence of an expensive night in his itinerary or because of a stock-out occurrence over his stay. We calculate the probabilities of these two incidents and then update the effective daily arrival rate, accordingly. In this way, we can use the classical single-night revenue management, even with multiple-night stays.

Equilibrium Mixed Strategies of Customers in an Unobservable Queue with Multiple Vacations

This paper studies and compares the equilibrium mixed strategies of customers with different decision criteria in an unobservable single-server queue with multiple vacations. Arriving customers can’t observe the queue length and the server state, whereas they are informed that the service time is exponentially distributed with unknown parameter, which is either an alternative of two values or belongs to a range. We consider three kinds of customers classified by their different waiting cost functions: linear, quadratic and exponential functions, and find that for the two types of partial information on service time parameter, both the equilibrium threshold expressions of customers’ effective arrival rates based on each criterion are consistent with each other except for the Laplace thresholds.

Cost analysis of a finite capacity queue with server breakdowns and threshold-based recovery policy

This paper analyzes a repairable M/M/1/N queueing system under a threshold-based recovery policy. The threshold-based recovery policy means that the server breaks down only if there is at least one customer in the system, and the recovery can be performed when q (1≤q≤N) or more customers are present. For this queueing system, a recursive method is applied to obtain steady-state solutions in neat closed-form expressions. We then develop some important system characteristics, such as the number of customers in the system, the probability that the server is busy, the effective arrival rate and the expected waiting time in the system, etc. A cost model is constructed to determine the optimal threshold value, the optimal system capacity and the optimal service rate at a minimum cost. In order to solve this optimization problem, the direct search method and Newton's method are employed. Sensitivity analysis is also conducted with various system parameters. Finally, we present some managerial insights through an application example.

Growth kinetics of GaAs nanoneedles on silicon and sapphire substrates

We study theoretically and experimentally the time evolution of GaAs nanoneedles grown by metal organic chemical vapor deposition on silicon and sapphire substrates. A theoretical model is presented which provides explicitly the nanoneedle length as a function of growth time under the assumption of a fixed aspect ratio. Experimental data confirms that the aspect ratio remains approximately constant during the growth. From fitting the experimental length-time dependences, we estimate the effective arrival rates and the Ga diffusion lengths as being 3.5 nm/min and 80 nm on the silicon and 2.9 nm/min and 400 nm on the sapphire substrates, respectively.

A packet buffer evaluation method exploiting queueing theory for wireless sensor networks

In large-scale wireless sensor networks (WSNs), when the consumption of hardware is limited, how to maximize the performance has become the research focus for improving transmission quality of service (QoS) of WSNs in recent years. This paper presents a new evaluation method for packet buffer capacity of nodes using queueing network model, whose packet buffer capacity is analyzed for each type node, when it is in the best working condition. In order to evaluate congestion situation in the queueing network, and to get real effective arrival rates and transmission rates in the model, holding nodes were added in the queueing network model, and equivalent queueing network model is expanded. We establish an M/M/1/N type queueing network model with holding nodes for WSNs and design approximate iterative algorithms. Experimental results show that the model is consistent with the real data.

Batch size modeling in a multi-item, discrete manufacturing system via an open queuing network

An open Queuing Network Analyzer (QNA) is often used in areas such as communication systems and discrete parts manufacturing systems. It uses the parametric decomposition method to approximately calculate the performance measures. The core of the method involves solving two systems of linear equations to calculate the first two moments of the effective arrival rate and service time. In this paper, we consider the effects of batch size on the parametric decomposition procedure of the QNA and modify the two sets of linear equations accordingly. The concept of a relative batch size is proposed for the purpose of modeling the effects of batch size. Experimental results are shown to illustrate the effectiveness of the method.

Database reorganization in parallel disk arrays with I/O service stealing

We present a model for data reorganization in parallel disk systems that is geared toward load balancing in an environment with periodic access patterns. Data reorganization is performed by disk cooling, i.e., migrating files or extents from the hottest disks to the coldest ones. We develop an approximate queueing model for determining the effective arrival rates of cooling requests and discuss its use in assessing the costs versus benefits of cooling actions.

Analyzing concurrent and fault-tolerant software using stochastic reward nets

We present two software applications and develop models for them. The first application considers a producer-consumer tasking system with an intermediate buffer task and studies how the performance is affected by different selection policies when multiple tasks are ready to synchronize. The second application studies the reliability of a fault-tolerant software system using the recovery block scheme. The model is incrementally augmented by considering clustered failures or the effective arrival rate of inputs to the system. We use stochastic reward nets, a variant of stochastic Pertri nets, to model the two software applications. In both models, each quantity to be computed is defined in terms of either the expected value of a reward rate in steady-state or at a given time θ, or as the expected value of the accumulated reward until absorption or until a given time θ. This allows extreme flexibility while maintaining a rigorous formalization of these quantities.