Capacity Queue Research Articles

An assessment of Fuzzy n-Policy queues with infinite capacity

This study examines the application of fuzzy n-policy queues with infinite capacity to optimize queuing systems under uncertain and variable conditions. Traditional queuing models often assume precise data, but real-world scenarios frequently involve ambiguity in parameters such as arrival rates, service rates, and system thresholds. The fuzzy n-policy model offers a more flexible approach by allowing these parameters to be represented as fuzzy variables, capturing the inherent uncertainty in complex queuing environments. By analyzing infinite capacity queues within this framework, the study evaluates system performance metrics like expected queue length, waiting time, and server utilization under different fuzzy set assumptions. The results demonstrate that the fuzzy nnn-policy enhances system responsiveness by adjusting service initiation thresholds based on the degree of uncertainty in arrival and service processes. These findings contribute to the broader field of stochastic and fuzzy queuing systems, providing practical insights for industries where demand variability and service uncertainty are prevalent, such as telecommunications, healthcare, and logistics.

Transient Analysis of a Finite Capacity Queueing System with Catastrophes and State-Dependent Environmental Change Parameter

This paper presents a transient analysis of a finite capacity queueing system with catastrophes and state-dependent environmental change parameter. The tendency of the Poisson rate at which the system moves from environmental state F to E increases or decreases as the number of customers in the queue. Also, at some random times, the number of customers is immediately reset to zero whenever a catastrophe occurs at the system. Transient solution is obtained by using the technique of probability generating function. The Steady state solution of the model is obtained by using the property of Laplace transform. Furthermore, we derive and discuss several particular cases of the queueing model, both with and without catastrophes.

Cost Analysis of a Finite Capacity Queue with Server Failures, Balking, and Threshold-Driven Recovery Policy

The study is on the cost dynamics which is concerned with finite queues in particular to susceptibility to server outages, threshold-driven recovery and Catastrophic events, but main focus is on balking behaviour of the customers. A thorough investigation of the financial implications of interruptions and efficacy to recovery strategies is done and to alleviate the impact of breakdowns, disasters and customer refusals the queue system designs through empirical research is conducted. Various recovery policies have been compared with the existing thresholds, and the study further endeavors to categorize the cost-effective approach to mitigate the economic concerns of server failures and catastrophic incidents. The study brings discernments on the expected development in the management of the queuing system along with the assistance in complete decision-making in cost efficiency and enhancement of the complete system performance.

Two-Level Full Factorial Design Approach for the Analysis of Multi-Lane Highway Section under Saturated and Unsaturated Traffic Flow Conditions

Oversaturation of highways occurs due to their inadequate assessment and design. In this paper, we propose both a mathematical queuing model and a Discrete-Event Simulation (DES) framework based on Newell’s triangular flow-density relationship for the performance analysis of a multi-lane highway section. The proposed framework is a finite capacity queuing system, which captures an increase in the flow with the vehicle density up to the capacity of the section in an unsaturated condition and a decrease in the flow in the case of a saturated condition, depicting the actual traffic conditions on the highway section. First, the Birth–Death Process is used to build the mathematical queuing model (BDP), and the average number of vehicles (average queue length) and blocking probability on the highway section are estimated. Then, the accuracy of the mathematical queuing model is verified by the proposed DES framework. The “significance and effects” of different design factors are evaluated using the two-level full factorial design technique. The analysis of the experimental results reveals that the length of the highway section and the number of lanes are the most significant factors affecting the average queue length and blocking probability, while the jam density only has a significant effect on the average queue length and does not affect the blocking probability. In case of a two-way interaction, the combined effect of the “length-lanes” significantly affects the average queue length. In the end, a multiple-factor linear regression model is also developed for the prediction of the average number of vehicles on the highway section based on the design factors.

Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience

We consider a non-standard class of Markovian time: varying infinite capacity queues with possibly heterogeneous servers and impatience. We assume that during service time, a customer may switch to the faster server (with no delay), when such a server becomes available and no other customers are waiting. As a result, customers in the queue may become impatient and leave it. Under this setting and with certain restrictions on the intensity functions, the quantity of interest, the total number of customers in the system, is the level-dependent birth-and-death process (BPD). In this paper, for the first time in the literature, explicit upper bounds for the distance between two probability distributions of this BDP are obtained. Using the obtained ergodicity bounds in combination with the sensitivity bounds, we assess the stability of BDP under perturbations. Truncation bounds are also given, which allow for numerical solutions with guaranteed truncation errors. Finally, we provide numerical results to support the findings.

MAP/PH/1 Üretim Envanter Modeli

In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (s,S) policy. The production is switched on when the inventory level depletes to s and the production remains on until the inventory level reaches to the maximum level S. Once the inventory level becomes S, the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory policy.

A meta-heuristic optimization for a novel mathematical model for minimizing costs and maximizing donor satisfaction in blood supply chains with finite capacity queueing systems

Blood and blood banks play an essential role in patient care. This study proposes a novel mathematical model for Blood Supply Chains (BSCs), which minimizes the total costs and maximizes donor satisfaction by reducing the system’s waiting time. The model addresses several aspects of the BSC, such as locating collection centers, allocating blood donors to collection centers, inventory control in the main blood center, blood shortage and deterioration considerations, and queueing systems in collection centers over a planning horizon. Queueing systems lead to a better understanding of the BSC and provide an opportunity to investigate donors’ attendance and waiting times. A real-world case study is presented and solved using a new meta-heuristic algorithm to illustrate the model’s applicability. Finally, sensitivity analyses are performed, and several beneficial managerial insights are provided.

Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy

In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the Nth customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.

On the age of information for non-preemptive queues in tandem

A monitoring system operates over a network of first-come, first-served queues in tandem, in which a source is transmitting its status to a monitor at the end of the tandem. To characterize the freshness performance of this monitoring system, we analyze the average Age of Information for this system, in which the status update arrivals are Poisson distributed and each queue is served by a non-preemptive, memoryless server. We first study the case of single-capacity queues that are modeled as a stochastic hybrid system, and we derive the average age for two queues with different service rates and three queues with equal service rate. We then study the infinite capacity queue case and use the graphical approach to derive the average age for two queues in tandem with equal service rates. Finally, we simulate the average age for intermediate cases of k capacity queues, which fall in between the two extreme cases of k = 1 and k = ∞.

Cost-Effective Service Chain Construction with VNF Sharing Model Based on Finite Capacity Queue

Cost-Effective Service Chain Construction with VNF Sharing Model Based on Finite Capacity Queue

Modified State-Dependent Queuing Model for the Capacity Analysis of Metro Rail Transit Station Corridor during COVID-19

The COVID-19 pandemic policies have had a significant impact on the daily commuter flow at the metro rail transit stations. In this study, we propose a modified state-dependent M(n)/G(n)/C/C queuing model for the analysis of commuter flow in the corridor of metro rail transit stations in the COVID-19 situation in order to ensure safe social distance. The proposed model is a finite capacity queuing system with state-dependent commuter arrivals and state-dependent service rates based on the flow–density relationship. First, a mathematical queuing model is developed by using the birth–death process (BDP) and the expected number of commuters, and average area occupied per commuter and blocking probabilities are computed. Then, the accuracy of the proposed model is verified by a discrete-event simulation (DES) framework. (1) The proposed model’s results are compared to those of the existing M/G(n)/C/C model. The proposed modified model’s sensitivity analysis revealed that the anticipated number of commuters in the corridor remains smaller when the arrival rate is state-dependent. (2) In accordance with COVID-19 protocol, when the facility is congested, commuters are discouraged from entering and a safe social distance is maintained between them. (3) No commuters are impeded, and adequate throughput is ensured from the corridor. The proposed model will assist the metro rail transit station operators in making intelligent decisions regarding the operations in the COVID-19 situation.

Evaluation of the end-to-end response times in an energy harvesting wireless sensor network using a receiver-initiated MAC protocol

In this paper we propose an analytical model for the evaluation of the end-to-end response time in an energy-harvesting wireless sensor network where the nodes use a receiver-initiated MAC protocol. Each individual node is modeled by means of a finite capacity queue with repeated server vacations of different types. The available energy is modeled by means of an extra variable. The system occupancy in a tagged node together with the available energy are observed at inspection instants, leading to a discrete-time Markov Chain. We derive closed form formulas for the system occupancy distribution at inspection instants and at arbitrary time instants together with the mean response time in this tagged node. The model is applied for the evaluation of the end-to-end response time a packet experiences when crossing different nodes in an energy-harvesting wireless sensor network. The model allows to determine important system parameters, such as the time a node listens to the medium to receive a beacon, the frequency of the transmission of beacons.

A queueing model for a wireless sensor node using energy harvesting

In this paper we propose a generic queueing model that can be used to evaluate the performance of a wireless sensor node that uses energy harvesting. The alteration of such a device between the transmit and sleep mode (or between consuming energy and harvesting energy), is modeled by means of a finite capacity queueing system with repeated server vacations. The duration of a service, resp. vacation, is determined by the available energy at the start of the service, resp. vacation. Therefor we introduce in the model a variable that keeps track of the available energy. The system occupancy and the available energy are observed at inspection instants (i.e., the end of a service or of a vacation), resulting in a discrete-time Markov Chain. We derive closed form formulas for the system occupancy distribution at inspection instants and at arbitrary time instants together with the Laplace transform of the waiting time distribution. The possible use of the model to evaluate the system’s performance for various parameter values is illustrated by means of a number of examples.

Stationary analysis of infinite queueing system with two-stage network server

As the world’s major economies and technologies have matured, they are dominated by service-focused approach leading to study and analysis of service models for improved understanding and efficiency. Research in this direction has been done on various parameters of the finite queues using different approaches. The study discussed in this paper deals with the stationary behavior of two-stage queuing system with infinite capacity where any arriving customer is serviced in two stages in a mutually exclusion fashion. The steady state system size probabilities for the infinite capacity queueing system with two stages of service are obtained in recursive form. Further, numerical interpretations are presented to depict the system behavior for values of the parameters.

Ergodicity bounds for the Markovian queue with time-varying transition intensities, batch arrivals and one queue skipping policy

In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and one special queue skipping policy. Customers arrive in batches but are served one by one in any order. The size of the arriving batch becomes known upon its arrival and at any time instant the total number of customers in the system is also known. According to the adopted queue skipping policy if a batch, which size is greater than the current total number of customers in the system, arrives, all customers currently residing in the system are removed from it and the new batch is placed in the queue. Otherwise the new batch is lost and does not have effect on the system. The distribution of the total number of customers in the system is under consideration under assumption that the arrival intensity λ(t) and/or the service intensity μ(t) are non-random functions of time. We provide the method for the computation of the upper bounds for the rate of convergence of system size to the limiting regime, whenever it exists, for any bounded λ(t) and μ(t) (not necessarily periodic) and any distribution of the batch size. For periodic intensities λ(t) and/or μ(t) and light-tailed distribution of the batch size it is shown how the obtained bounds can be used to numerically compute the limiting distribution of the queue size with the given error. Illustrating numerical examples are provided.

Sustainable traffic management and control system for arterial with contraflow left-turn lanes

Nowadays, air pollution caused by traffic congestion has progressively drawn more and more attention. This paper proposes a traffic management and control platform from the perspective of sustainable development to reduce both vehicle emission and delay along arterial with contraflow left-turn lane (CLL). Unlike the traditional intersection layout and the control strategy, the existence of the contraflow left-turn lanes at intersections brings difficulties in setting phase sequences due to the complex interactions among upstream and downstream lanes. Furthermore, the queueing conditions are totally different from traditional intersections due to the complex queueing phenomenon between pre-signals and main signals. A macroscopic traffic model is proposed to model the intersection along arterial with CLL and is established on the basis of finite capacity queueing models. The optimization framework derives fixed-time traffic signal control plans, in which the green splits of the main signal and the pre-signal are explicitly considered. The nondominated sorting genetic algorithm II (NSGA-II) is employed to solve problem. A case study based on the field data of four intersections along the West Yan’an Road in the city of Shanghai is carried out to investigate the performance of the proposed framework. The microscopic simulator AIMSUN is used to evaluate and compare the travel delay and vehicle emissions obtained by the newly proposed signal plans and the signal plans derived by using traditional traffic control method. The simulation results indicate that the proposed framework successfully reduce travel delay and vehicle emission at intersections along arterial road with CLL.

AGV or Lift-AGV? Performance trade-offs and design insights for container terminals with robotized transport vehicle technology

New container terminals are embracing robotized transport vehicles such as lift-automated guided vehicles (LAGVs) and automated guided vehicles (AGVs) to enhance the terminal throughput capacity. Although LAGVs have a high container handling time, they require less coordination with other terminal equipment in comparison with AGVs. In contrast, AGVs are hard-coupled resources, require less container handling times, but operate with high coordination delays in comparison with LAGVs. The effect of such operational trade-offs on terminal performance under various design parameter settings, such as yard block layout and a number of resources, is not well understood and needs to be evaluated at the terminal design phase. To analyze these trade-offs, we develop stylized semi-open queuing network models, which consist of two-phase servers and finite capacity queues. We develop a novel network decomposition method for solving the proposed queuing models. The accuracy of the solution method is validated using detailed simulation models. Using the analytical models, we study the performance trade-offs between the transport vehicle choices: LAGVs and AGVs. Our results show that the throughput capacity of the terminal in the container unloading process increases by up to 16% if LAGVs are chosen as transport vehicles instead of AGVs. However, at certain parameter settings, specifically, when the arrival rate of containers is low, the throughput time performance of the terminal is higher (up to 8%) with AGVs than with LAGVs. We also derive insights on the yard block layout and the technology choice for quay cranes.

Optimal and Sensitivity Analysis of Vacation Queueing System with F-Policy and Vacation Interruption

In this article, the investigation on a randomized arrival control policy for the prospective customers in the finite capacity queueing system with working vacation and vacation interruption is done. The impatience behavior of the customers is also considered in modeling and assumptions to the studied problem to make it more realistic. In the investigated queueing model, at the epoch when the number of customers in the system reaches system’s capacity, newly arriving customers are not allowed to join the system for service and referred as lost customers. As the length of the queue decreases to a pre-specified threshold value F, the server commences a start-up for allowing to join the customers according to an exponential distribution and starts allowing newly arriving customers to join the system for service. The steady-state probability distribution and vector representation of various system performance measures are derived using matrix-analytic approach. The cost optimization problem is also formulated, and the particle swarm optimization algorithm is implemented to determine the optimal decision parameters to achieve the minimal expected cost. Finally, some numerical results in tables and graphs are provided for the illustrative and comparative purpose which help the system analyst in decision making from the performance and economic perspective.

A Geo/Geo/1 Inventory Priority Queue with Self Induced Interruption

This paper considers discrete time (s, S) inventory Geo/Geo/1 priority queue formed by the customers’ induced interruption during service. An arriving customer enters into a high priority queue of infinite capacity. During his/her service, the service may be interrupted due to own reasons with some probability. The interrupted customer is moved to a lower priority queue of infinite capacity. An item in the inventory is supplied whenever a customer leaves from high priority queue after interrupting/completing the service. The customer in the lower priority queue is served according to preemptive priority discipline. Inter-arrival time, service time and lead time are considered to be geometrically distributed. We use the matrix analytic method to analyse the model. The necessary and sufficient condition for the stability of the system is obtained. The marginal distributions of both higher and lower priority queue lengths are studied. Numerical experiments are incorporated to draw special attention to the importance of the model.

Matrix-geometric solution of multi-server queueing systems with Bernoulli scheduled modified vacation and retention of reneged customers: A meta-heuristic approach

ABSTRACT In the present article, we deal with the multi-server finite capacity queueing system with Bernoulli’s scheduled modified vacation policy and the realistic retaining policy of reneged customers. After completion of the service of any customer, the server decides whether to go for the vacation of random duration or to continue facilitating the service to the waiting customer, if any, present in the queue. All servers, homogeneous in nature, provide the state-dependent service following the threshold policy to reduce the overload of the system. The impatience behavior of customers like balking and reneging is also considered in the stochastic modeling of the studied problem. The matrix analytic approach is employed to obtain the steady-state probabilities with which various system performance measures are also developed with practical justification. Finally, the expected cost minimization problem is formulated and dealt with the meta-heuristic approach: particle swarm optimization (PSO). All results of numerical simulation and optimal analysis are summarized in tables and graphs to provide quick insight. The concluding remarks and future scopes have also been discussed.