Queueing Behavior Research Articles

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

In this paper, we consider a discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system. A more flexible switching mechanism between low and regular service states is introduced to enhance the practical value of the working vacation queue. Under different precision levels of the system information, namely observable, almost unobservable and fully unobservable cases, the utility function is studied from both the individual customer's and the system administrator's points of view. By analyzing the steady-state behavior of the system, the associated optimal joining decisions under different information scenarios are obtained. We find that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period. A similar situation also appears in almost unobservable case. Such phenomenon is not possible for the classic first come first served queue due to the fact that there is no vacation time and thus will not cause large fluctuations in customers' conditional waiting time. Additionally, we also conduct some numerical comparisons to demonstrate the effect of the information levels as well as system parameters on customer joining behavior.

Probabilities of Large Deviations for a Queue with Regenerative Input Flow

We consider a single-channel queueing system with unlimited queue and regenerative input flow. Conditions under which there exists a nonzero logarithmic limit for probabilities of large deviations of waiting time at steady-state are obtained. It is shown that the asymptotic behavior of a large queue in the steady state is determined by the joint distribution of the regeneration period of the input flow and the number of claims received during this period, and it does not depend on the distribution of arrival times of claims within the regeneration period.

Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically.

Comparisons of Perceptions and Behavior in Ticket Queues and Physical Queues

Ticket queues are systems that issue tickets to customers upon their arrival. Although ticket queues are preferred by many service providers, there is limited research on ticket queues, especially on customer perceptions of, preferences for, and behavior in these systems. We conducted a series of surveys to understand customer preferences and patience in a ticket queue and a physical queue (stand-in-line system) and to investigate whether the assumptions used in analytical queuing models for customer abandonment behavior are realistic. Study results indicate that subjects generally prefer ticket queues over physical queues and have greater patience in ticket queues than they do in physical queues. In addition, we observe that subjects are willing to wait longer than they initially were, assuming that they already have spent some time waiting in line. Using the survey results, we ran a series of simulation models by adjusting the traditional queuing assumptions and showed the impact of customer behavior on system performance measures in ticket and physical queues. Our results can assist managers, in determining the type of queue to implement under various service settings, and researchers, in modeling more realistic queuing systems.

Rational Abandonment from Priority Queues: Equilibrium Strategy and Pricing Implications

Observable priority queues are prevalent in practice and create incentives for utility-maximizing customers to abandon after joining. However, the literature has so far ignored this behavior and the resulting system control issues. This paper studies the rational abandonment behavior of utility-maximizing customers in the context of an observable two-class priority queue, and identifies novel implications. We characterize the equilibrium abandonment strategy of low-priority customers and show that it has a threshold structure that depends on the fee structure. We then consider pricing as a means to control the balking and abandonment behavior, both under welfare maximization and revenue maximization. Our pricing results highlight the importance of the timing of payments. We show that welfare-maximization requires charging only a service fee and no entrance fee. In contrast, revenue maximization generally requires a combination of both an entrance and a service fee. This two-fee structure is equivalent to charging only upon entrance but offering a partial cancellation refund. Moreover, charging only an entrance fee may generate more or less revenue than charging only a service fee, but the performance of the latter policy is more robust. This appears to be the first paper that (i) gives an analytical characterization of equilibrium abandonment behavior in observable priority queues, and (ii) studies pricing for any queueing system in presence of rational customer abandonment.

A DEC-MDP model for joint uplink/downlink resource management in OFDMA-based networks

With the advent of mobile services with asymmetric and symmetric quality of service (QoS) requirements, traditional single link resource allocation techniques have started to show some limitations in handling the complex requirements. To address these issues, joint uplink/downlink resource management approaches were recently introduced where both communications links are jointly considered in the resource management process. One direct consequence of this coupling is a modification of the underlying queueing behavior since the decision making process in one direction in terms of transmission rate now depends on the performance achieved in the opposite direction. In this paper, we present a modeling approach of the decision making process that takes place under the joint uplink/downlink resource management framework. Using decentralized Markov decision processes (DEC-MDP) as a model and gradient ascent methods as an optimization technique, we formulate and solve the joint uplink/downlink decision making process. The uplink and downlink of each user are considered as agents. Assuming certain subcarrier and power allocation schemes, we investigate the resource usage in the uplink and downlink to achieve a certain delay balancing constraint where the total delay in the uplink and downlink is bound by a pre-determined threshold. The approach followed starts by modeling the problem in hand using DEC-MDPs. After discussing the different aspects of the model, the solution using gradient ascent is described. Simulation results illustrate the different dimensions of the problem and their impact on the resource management process.

Identifying potential bottlenecks in production systems using dual prices from a mathematical programming model

The importance of identifying bottlenecks in production systems for effective production control and continuous improvement is well recognised. A useful definition of a bottleneck is the station to whose performance the performance of the overall production system is most sensitive. However, obtaining accurate estimates of the impact of changes in a given station's performance on the performance of a production system is often difficult. This paper uses the dual prices associated with production resources in a production planning model to support the identification of bottlenecks as the product mix in the system changes over time. The planning model considers queueing behaviour at production resources using non-linear clearing functions. Relationships between the dual prices of different resources are derived, and the bottleneck information obtained is compared to that from a model that does not consider queueing behaviour.

Dynamics of Order Positions and Related Queues in a Limit Order Book

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a corollary, explicit analytical expressions for various quantities of interests in a limit order book are derived.

Embedded Markov chain approach to retrial queue with vacation, phase repair and multioptional services

The investigation deals with the steady-state behavior of a batch arrival retrial queue with multi-optional services and phase repair under Bernoulli vacation schedule. The customers enter the system in batches and are admitted following Bernoulli admission control policy. The incoming customers are forced to join the retrial group if they find the server unavailable. The customers are served in two phases viz. first essential service (FES) followed by second optional services (SOS). The server is unreliable and if fails, it is repaired in d-compulsory phases so as to become as good as before failure. The server may go for a vacation after each service completion following Bernoulli vacation schedule or it may continue serving the next customer. By applying the embedded Markov chain method, we establish the ergodicity condition for the system. The steady-state formulae for some queueing measures are established by evaluating the generating functions of queue length distribution. The cost function of the system has also been formulated. Finally, the effects of various parameters on the performance of the system have been examined numerically.

On the exact transient solution of fluid queue driven by a birth death process with specific rational rates and absorption

Birth death processes with rational birth and death rates have been studied by Maki (1976). In this paper a fluid queue driven by a birth death process with infinite state space and absorption is studied where the birth and death rates are rational functions of linear polynomials. We obtain an explicit transient solution for the fluid queue model using continued fraction approach to solve the underlying system of partial differential equations. For specific value of the parameter the considered model reduces to the model discussed by Parthasarathy, Sericola and Vijayashree (2005) and the results coincide. We also analyze the behavior of the fluid queue in a long run.

Time-delayed follow-the-leader model for pedestrians walking in line

We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting model can be used either for modeling pedestrian queuing behavior or can be incorporated into bi-dimensional models of pedestrian traffic.

Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations

This paper studies the customers’ equilibrium balking behavior in some single-server Markovian queues with two-stage working vacations. That is, the server starts taking two successive working vacations when the system becomes empty, during which he provides low-rate service but maintains different service rates in the two-stage vacations. Based on different precision levels of system information, we discuss observable queues, partially observable queues and unobservable queues, respectively. For each type of queues, we get the customers’ equilibrium balking strategy and equilibrium social welfare per time unit, and numerically observe that their positive equilibrium strategy is unique. Especially, for partially observable queues, the customers’ equilibrium joining probabilities in vacation states are not necessarily smaller than that in busy state.

Using formal reasoning on a model of tasks for FreeRTOS

Abstract FreeRTOS is an open-source real-time microkernel that has a wide community of users. We present the formal specification of the behaviour of the task part of FreeRTOS that deals with the creation, management, and scheduling of tasks using priority-based preemption. Our model is written in the Z notation, and we verify its consistency using the Z/Eves theorem prover. This includes a precise statement of the preconditions for all API commands. This task model forms the basis for three dimensions of further work: (a) the modelling of the rest of the behaviour of queues, time, mutex, and interrupts in FreeRTOS; (b) refinement of the models to code to produce a verified implementation; and (c) extension of the behaviour of FreeRTOS to multi-core architectures. We propose all three dimensions as benchmark challenge problems for Hoare’s Verified Software Initiative.

G-RAND: A phase-type approximation for the nonstationary [formula omitted] queue

We present a Markov model to analyze the queueing behavior of the nonstationary G(t)/G(t)/s(t)+G(t) queue. We assume an exhaustive service discipline (where servers complete their current service before leaving) and use acyclic phase-type distributions to approximate the general interarrival, service, and abandonment time distributions. The time-varying performance measures of interest are: (1) the expected number of customers in queue, (2) the variance of the number of customers in queue, (3) the expected number of abandonments, and (4) the virtual waiting time distribution of a customer arriving at an arbitrary moment in time. We refer to our model as G-RAND since it analyzes a general queue using the randomization method. A computational experiment shows that our model allows the accurate analysis of small- to medium-sized problem instances.

Simulation : Analysis of Single Server Queuing Model

A queue is a line of people or things to be handled in a sequential order. It is a sequence of objects that are waiting to be processed. Queuing theory is the study of queues for managing process and objects. Simulation has been applied successfully for modeling small and large complex systems and understanding queuing behavior. Analysis of the models helps to increases the performance of the system. In this paper we analyze various models of the Single server queuing system with necessaryimplementation using Matlab Software.

Balancing Queueing Systems With Excess Demand

In a rough economic environment and increased competition, one issue critical to many businesses is to achieve an optimum balance between supply and demand. Double-ended queuing structure, where demand and supply occur simultaneously, can be utilized to model various manufacturing and service activities. By associating costs per time unit due to a unit of excess of supply or demand, the total cost will include now costs due to imbalance of demand and supply. The authors examine the queuing behavior and how to minimize the above total cost by advanced planning aimed to hold imbalance costs at a minimum.In this paper, the main focus will be on situations where a stochastic system has become unstable due to demand exceeding supply. To determine how sensitive optimal solutions are to changes in model parameters, for each policy, either decreasing demand or increasing supply, exact optimal solutions were found for a large number of scenarios and then used this scenarios database to fit the best possible regression model. The paper ends illustrating the use of the model to research funding where typically proposals compete for scarce funding resources.

Effects of state-dependent balking on multi-server non-stationary queueing systems

A combination of discrete-time modelling and theoretical analysis is used to develop an easy-to-use Normal approximation for the time-dependent behaviour of multi-server queueing systems subject to state-dependent balking. Key findings that underpin the approximation are that time lags between peaks in arrival rates and congestion levels can be ignored; queue behaviour is insensitive to distribution of service time beyond its mean; and distribution of number in the system is near Normal. This model is then used to derive valuable management implications for service-orientated systems where delays are frequent and abandonments are an important feature. Key insights are that such systems can often adopt very ‘sub-optimal’ behaviour, and that customer impatience can be very beneficial where management wishes to improve system performance. ‘Optimal’ performance is defined, and practical measures for queue managers to move system performance towards ‘optimality’ are identified.

Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process

This paper applies a matrix-analytical approach to analyze the temporal behavior of Markovian-modulated batch-service queue with discrete-time batch Markovian arrival process (DBMAP). The service process is correlated and its structure is presented through discrete-time batch Markovian service process (DBMSP). We examine the temporal behavior of packet loss by means of conditional statistics with respect to congested and noncongested periods that occur in an alternating manner. The congested period corresponds to having more than a certain number of packets in the buffer; noncongested period corresponds to the opposite. All of the four related performance measures are derived, including probability distributions of a congested and noncongested periods, the probability that the system stays in a congested period, the packet loss probability during congested period, and the long term packet loss probability. Queueing systems of this type arise in the domain of wireless communications.

A Closed-Form Model for the IEEE 802.3az Network and Power Performance

We propose an analytical model able to accurately estimate both power consumption and network performance indexes of Energy Efficient Ethernet (EEE) links working at the three available speeds under various traffic load patterns and packet size distributions. The model is sufficiently flexible and accurate to consider different traffic parameters; among others, the packet size distribution, the average burst inter-arrival rate, the burst size distribution, etc. With relatively low complexity, since it addresses stationary queue behavior, the analysis allows obtaining the average energy consumption of the link and, unlike previous works, the mean latency time experienced by incoming packets in closed form, without any upper or lower bound approximations. This aspect makes the model suitable to be adopted in optimization frameworks for network design and control purposes. The numerical results of the model are validated against measurements on a real test bench.

Novel methods of utilizing Jitter for Network Congestion Control

This paper proposes a novel paradigm for network congestion control. Instead of perpetual conflict as in TCP, a proof-of-concept first-ever protocol enabling inter-flow communication without infrastructure support thru a side channel constructed on generic FIFO queue behaviour is presented. This enables independent flows passing thru the same bottleneck queue to communicate and achieve fair capacity sharing and a stable equilibrium state in a rapid fashion.