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In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace–Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system. [ABSTRACT FROM AUTHOR]

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system. [ABSTRACT FROM AUTHOR]

We study a financial market where the risky asset is modelled by a geometric Itô-Lévy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow and Protter (J Bank Finan 29:2803–2820, 2005) for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas and Shreve (Methods of Mathematical Finance, Springer, Berlin, 1998) (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system. In this paper we consider a jump diffusion market model with a singular drift term modelled as the local time of a given process, and with a delay θ > 0 in the information flow available for the trader. We allow the stock price dynamics to depend on both a continuous process (Brownian motion) and a jump process (Poisson random measure). We believe that jumps and delays are essential in order to get more realistic financial market models. Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as θ > 0 . This implies that there is no arbitrage in the market in that case. However, when θ goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay. Our model is also relevant for high frequency trading issues. This is because high frequency trading often leads to intensive trading taking place on close to infinitesimal lengths of time, which in the limit corresponds to trading on time sets of measure 0. This may in turn lead to a singular drift in the pricing dynamics. See e.g. Lachapelle et al. (Math Finan Econom 10(3):223–262, 2016) and the references therein. [ABSTRACT FROM AUTHOR]

We consider a model describing the length of two queues that incorporates customer choice behavior based on delayed queue length information. The symmetric case, where the values of the time-delay parameter in each queue are the same, was recently studied. It was shown that under some conditions, the stable equilibrium solution becomes unstable as the common time delay passes a threshold value. This one-time stability switch occurs only at a symmetry-breaking Hopf bifurcation where a family of stable asynchronous limit-cycle solutions arise. In this paper, we examine the non-symmetric case, wherein the values of the time-delay parameter in each queue are different. We show that, in contrast to the symmetric case, the non-symmetric case allows bubbling, multiple stability switches and coexistence of distinct families of stable limit cycles. An investigation of the dynamical behavior of the non-symmetric system in a neighborhood of a double-Hopf bifurcation using numerical continuation explains the occurrence of the bistable limit cycles. Quasi-periodic oscillations were also observed due to the presence of torus bifurcations near the double-Hopf bifurcation. These identifications of the underlying mechanisms that cause unwanted oscillations in the system give a better understanding of the effects of providing delayed information and consequently help in better management of queues.

Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] can be rigorously obtained as a functional law of large numbers limit of a stochastic queueing process, and we generalize their threshold analysis to arbitrary dimensions. Moreover, we prove a functional central limit theorem for the queue length process and show that the scaled queue length converges to a stochastic delay differential equation. Thus, our analysis sheds new insight on how delayed information can produce unexpected system dynamics. [ABSTRACT FROM AUTHOR]

We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When information on demand is modeled by a delayed diffusion process, we also show that this intermediate regime collapses to a single equilibrium while the other regimes approximate the deterministic setting as the delay tends to zero. Moreover, as the delay approaches zero, the unique equilibrium achieved in the stochastic case provides a way to select a natural equilibrium within the range observed in the no lag setting. Numerical illustrations are presented when demand is modeled by an Ornstein–Uhlenbeck process and price is an affine function of output. [ABSTRACT FROM AUTHOR]

Under certain conditions, pigeons prefer information about whether food will be forthcoming at the end of an interval to a higher chance of obtaining the food. In the typical protocol, choosing one option (Informative) is followed by one of two 10-s long terminal-link stimuli: SG always ending in food or SR never ending in food, with SG occurring only 20% of the trials. The other option (Non-informative) is also followed by one of two 10-s long terminal-link stimuli: SB or SY, both ending in food 50% of the trials. Although the Informative option yields food with a lower probability than the Non-informative (0.2 vs. 0.5), pigeons prefer it. To determine whether such preference occurs because SG and SR disambiguate the trial outcome immediately upon choice, we delayed the moment the disambiguation took place in two experiments. In Experiment 1, when the Informative option was chosen, SG always ensued for t seconds of the terminal-link, and then the standard contingencies followed. Experiment 2 was similar, except that SR always ensued for t seconds. Across conditions, t varied from 0 to 10 s. In both experiments, preference for the Informative option decreased with t , but the effect was stronger in Experiment 1. We discuss the implication of these findings for functional and mechanistic models of suboptimal choice. • Pigeons often prefer leaner but informative options over richer but noninformative ones. • We explore if immediate trial outcome disambiguation is a crucial factor for these preferences. • In two experiments, we delayed disambiguation when the informative option was chosen. • Longer delays to disambiguation yielded weaker preferences. • The effect was stronger when the pre-disambiguation period involved exposure to the food-signaling stimulus. [ABSTRACT FROM AUTHOR]

This study proposes a novel distributed economic model predictive control (EMPC) strategy for energy‐efficient cooperative formation of decoupled multi‐agent non‐linear systems with transmission delay. In this system, each subsystem is controlled to maximise the economic performance during tracking the reference trajectory and maintaining its relative position to the neighbouring subsystems. The cooperation between subsystems is executed through the cost functions and coupled constraints associated with the delayed information. A Lyapunov‐based contractive constraint is introduced to establish recursive feasibility of the proposed EMPC strategy. Moreover, stability of any single subsystem with the EMPC is proved rigorously by exploiting the idea of input‐to‐state stability and for both strongly and weakly connected networks, stability of the whole system is then proved by using the generalised small gain condition. The effectiveness of the proposed strategy is illustrated by two numerical simulation experiments. [ABSTRACT FROM AUTHOR]

The data transmission performance of a network protocol is closely related to the amount of available information about the network state. In general, more network state information results in better data transmission performance. However, acquiring such state information expends network bandwidth resource. Thus, a trade-off exists between the amount of network state information collected, and the improved protocol performance due to this information. A framework has been developed in the previous efforts to study the optimal trade-off between the amount of collected information and network performance. However, the effect of information delay is not considered in the previous analysis. In this paper, we extend the framework to study the relationship between the amount of collected state information and the achievable network performance under the assumption that information is subject to delay. Based on the relationship we could then obtain the optimal resource allocation between the data transmission and network state information acquisition in a time-varying network. We have considered both memoryless and memory-exploited scenarios in our framework. Structures of the Pareto optimal information collection and decision-making strategies are discussed. Examples of multiuser scheduling and multi-hop routing are used to demonstrate the framework’s application to practical network protocols. [ABSTRACT FROM AUTHOR]

Recommendation system is widely used because of its personalized service. It helps users obtain satisfactory results due to ambiguous expression in search engines. However, with the increasing number of users and items, most of the existing recommendation algorithms have problems of cold start, sparse data and high complexity. To address the above issues, this paper applies the rating information and attribute information of users and items to better represent the preferences of users and the activity of items by enriching the available information. Furthermore, we propose a novel game-based evolutionary clustering method to divide interest communities for users, which not only reduces the complexity of recommendation, but also takes full account of users' preferences. In addition, the impact of delayed information transmission on experimental performance is considered in the game-based evolutionary clustering. Since the calculation of similarity plays a significant role in finding the nearest neighbors of target users in the community, we propose a new similarity measurement strategy based on user preferences. Finally, the effectiveness of the proposed algorithm is verified by ablation experiment and comparison experiments. The experimental results illustrate that our algorithm outperforms the existing excellent algorithms. • Rating and attribute information are fused to better represent the preferences of users. • Game-based evolutionary clustering is designed to divide users with similar hobbies. • Delayed information transmission is considered in the game-based clustering methods. • Similarity index based on user preferences is used in the collaborative filtering. [ABSTRACT FROM AUTHOR]

This study investigates the output consensus problem for a class of non‐linear networked multi‐agent systems with switching topology and time‐varying delays. To synchronise the outputs of the agents, novel distributed data‐driven consensus protocols are proposed, where the reference input is designed to be the time‐varying average of the agents' output. To avoid the self‐tracking phenomenon, the delayed information is introduced in the protocol. The proposed methods merely depend on the input and output data of the neighbouring agents, without using explicit or implicit information of its mathematical model. Sufficient conditions are derived to guarantee the closed‐loop stability and consensus, with the convergence rate obtained. Numerical and practical examples are conducted to demonstrate the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of angle-of-arrival (AOA) target tracking in the three-dimensional (3D) space using multiple distributed sensors. Some sensors cannot share information directly because of the communication distance constraint arising from the broadcast power limitation of communication equipment. This can lead to reduced estimation performance as a result of limited information exchange. To improve the estimation performance, delayed information transmitted by intermediate sensors through multiple hops is utilized. A neighborhood matrix is proposed to sort the received information in terms of the number of hops. The information is classified into current information, 1-step delayed information and multi-step delayed information. A distributed pseudolinear Kalman filter (DPLKF) is developed based on out-of-sequence measurement updates to process the current and delayed information. Simulation examples demonstrate the effectiveness of the proposed algorithm in improving the tracking performance, in particular, during the initial convergence phase. [ABSTRACT FROM AUTHOR]

We consider a distributed consensus problem over a network, where at each time instant every node receives two pieces of information from disjoint neighboring sets: a weighted average of current states of neighbors from a primary network, and a weighted average of one-hop delayed states of neighbors from a secondary network. The proposed algorithm makes each node update its state to a weighted average of these individual averages. We show that convergence to consensus is guaranteed with non-trivial weights. We also present an explicit formula for the weights allocated to each piece of the information for the optimal rate of convergence, when the secondary network is the complement of the primary network. Finally numerical examples are given to explore the case when the neighbor sets of the agents do not cover the whole network. [ABSTRACT FROM AUTHOR]

This study addresses a distributed H∞ filtering problem for discrete‐time Takagi–Sugeno fuzzy complex networks with sensor saturation, where nodes and filters are connected via a shared communication network. It is supposed that each node's output measurement transmitted to its filter according to Round‐Robin scheduling protocol. Based on a non‐parallel distributed compensation strategy, distributed filters are constructed, where the coupling matrix between filters could be different from the one between nodes and the parameters of the filters depend on current and delayed membership functions. The augmented filtering error system is represented as a discrete‐time fuzzy system with time‐varying delays. By applying a novel nonquadratic Lyapunov functional that depends on current and delayed membership functions, and combined with a Abel lemma‐based finite‐sum inequality, distributed regional H∞ filters are designed such that the local and exponential stability of the augmented filtering error system is ensured and the H∞ performance requirement is satisfied. Numerical examples illustrate the effectiveness and less conservatism of the proposed method. [ABSTRACT FROM AUTHOR]

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer. [ABSTRACT FROM AUTHOR]

The search for information in memory of technological competition process in the market is analysed using techniques widespread in biomathematics. Here we examined the effects that delayed information causes in choosing strategies process on the part of manufacturers to supplant a technology by introducing an alternative one. A differential-equation system with delays is presented to describe the dynamics of an endogenous model with memory. Situations of competition in which the market has several manufacturers using the same technologies and are in competition are analyzed. Conditions for stability and existence of periodic oscilations by means of Hopf bifurcation is investigated. [ABSTRACT FROM AUTHOR]

Abstract: In intelligent transport system, some advanced information feedback strategies have been developed to reduce the oscillations and enhance the capacity on the road level. However, seldom strategies have considered the information delay and user equilibrium (UE) objective. Here, a derivative cost feedback strategy (DCFS) is proposed to reduce the influence of the delay, based on the UE principle. The simulation results show that in both no-delay and delay information cases, DCFS are the best and can make the system reaching the UE. Because DCFS can predict the trend of the travel cost. [Copyright &y& Elsevier]

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller's price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively. [ABSTRACT FROM AUTHOR]

We study the problem of distributed scheduling in wireless networks, where each node makes individual scheduling decisions based on heterogeneously delayed network state information (NSI). This leads to inconsistency in the views of the network across nodes, which, coupled with interference, makes it challenging to schedule for high throughputs. We characterize the network throughput region for this setup, and develop optimal scheduling policies to achieve the same. Our scheduling policies have a threshold-based structure and, moreover, require the nodes to use only the 'smallest critical subset' of the available delayed NSI to make decisions. In addition, using Markov chain mixing techniques, we quantify the impact of delayed NSI on the throughput region. This not only highlights the value of extra NSI for scheduling, but also characterizes the loss in throughput incurred by lower complexity scheduling policies which use homogeneously delayed NSI. [ABSTRACT FROM AUTHOR]

We consider a model describing the length of two queues that incorporates customer choice behavior based on delayed queue length information. The symmetric case, where the values of the time-delay parameter in each queue are the same, was recently studied. It was shown that under some conditions, the stable equilibrium solution becomes unstable as the common time delay passes a threshold value. This one-time stability switch occurs only at a symmetry-breaking Hopf bifurcation where a family of stable asynchronous limit-cycle solutions arise. In this paper, we examine the non-symmetric case, wherein the values of the time-delay parameter in each queue are different. We show that, in contrast to the symmetric case, the non-symmetric case allows bubbling, multiple stability switches and coexistence of distinct families of stable limit cycles. An investigation of the dynamical behavior of the non-symmetric system in a neighborhood of a double-Hopf bifurcation using numerical continuation explains the occurrence of the bistable limit cycles. Quasi-periodic oscillations were also observed due to the presence of torus bifurcations near the double-Hopf bifurcation. These identifications of the underlying mechanisms that cause unwanted oscillations in the system give a better understanding of the effects of providing delayed information and consequently help in better management of queues. [ABSTRACT FROM AUTHOR]

Micromachines and nanoscale devices can act together for high-resolution monitoring and action on multiple size scales within physical materials and biological organisms. Such multiscale systems require robust distributed controls responsive to heterogeneous and poorly characterized microenvironments. To develop such controls, this paper extends the partially observable Markov decision process formalism to machines operating asynchronously at multiple scales and with delays. We show how an approximation to this formalism readily provides aggregate performance measures needed for designing distributed controls. This approach identifies the aggregate behavior as arising from differential-delay equations approximating the system’s dynamics. We illustrate this approach to distributed controls for chemical sensor networks consisting of micro- and nanoscale devices in the context of high-resolution biomedical diagnostics and treatment through localized drug delivery. [ABSTRACT FROM AUTHOR]

A controller with an unlimited buffer receives messages to be dispatched to c servers downstream in the network. However, the queue sizes at the individual servers are not known exactly, since information on each service completion reaches the controller only after some random delay. The controller can dispatch messages as soon as they arrive, in a cyclic manner, to the c servers. Alternatively, s/he can wait until full information is gained and dispatch a waiting message to a server only when s/he is sure that the server is free. Another strategy is to maintain a limited intermediate buffer in front of the servers, and forward messages to this buffer when information on service completion reaches the controller. If a server completes a job and the intermediate buffer is non-empty, it starts serving a job from this buffer with no delay. Such situations are common in many real life processes (such as passport control procedures, or at large waiting rooms in public offices) where customers wait, in front of c servers, to be served. A customer walks (=delay) to the next idle server when s/he sees her/his “waiting number” flashing on the screen. We analyze this model when the underlying process is the M/M/c queue and the information delay is exponential. We use both: i) probability generating functions of the multi-dimensional state space to calculate the boundary probabilities, and ii) matrix geometric approach to derive the stability condition of the system. We show that the intermediate buffer scheme reduces queue sizes and waiting times. Numerical examples are presented. [ABSTRACT FROM AUTHOR]

Dynamic Arrow-type price dynamics are investigated in a continuous time framework. The existence of a unique equilibrium is first proved under realistic conditions. Then, the local asymptotic stability of the equilibrium in the presence of instantaneous price and output information is shown. Continuously distributed time lags are then assumed in obtaining and implementing price and output information, or equivalently, it may be assumed that the firms and/or the market wants to react to long term effects rather than to follow sudden changes in price or outputs. If a time lag is assumed only in estimating the demand in the market, then the local asymptotic stability of the equilibrium is preserved. If the producers also use delayed information, then instability may occur. Stability conditions are derived and in the case of bifurcation the possibility of the birth of limit cycles is explored. [Copyright &y& Elsevier]

A class of prescribed duration pursuit–evasion problems with first-order acceleration dynamics and bounded controls is considered. In this class, the pursuer has delayed information on the lateral acceleration of the evader, but knows perfectly the other state variables. Moreover, the pursuer applies a strategy derived from the perfect information pursuit–evasion game solution. Assuming that the evader has perfect information on all the state variables as well as on the delay of the pursuer and its strategy, an optimal evasion problem is formulated. The necessary optimality conditions indicate that the evader optimal control has a bang–bang structure. Based on this result, two particular cases of the pursuer strategy (continuous and piecewise continuous in the state variables) are considered for the solution of the optimal evasion problem. In the case of the continuous pursuer strategy, the switch point of the optimal control can be obtained as a root of the switch function. However, in the case of the piecewise continuous (bang–bang) pursuer strategy, this method fails, because of the discontinuity of the switch function at this very point. In this case, a direct method for obtaining the switch point, based on the structure of the solution, is proposed. Numerical results illustrating the theoretical analysis are presented leading to a comparison of the two cases. [ABSTRACT FROM AUTHOR]

We study the behavior of a single-server discrete-time queue with batch arrivals, where the information on the queue length and possibly on service completions is delayed. Such a model describes situations arising in high speed telecommunication systems, where information arrives in messages, each comprising a variable number of fixed-length packets, and it takes one unit of time (a slot) to transmit a packet. Since it is not desirable to attempt service when the system may be empty, we study a model where we assume that service is attempted only if, given the information available to the server, it is certain that there are messages in the queue. We characterize the probability distribution of the number of messages in the queue under some general stationarity assumptions on the arrival process, when information on the queue size is delayed K slots, and derive explicit expressions of the PGF of the queue length for the case of i.i.d. batch arrivals and general independent service times. We further derive the PGF of the queue size when information on both the queue length and service completion is delayed K=1 units of time. Finally, we extend the results to priority queues and show that when all messages are of unit length, the cμ rule remains optimal even in the case of delayed information. [ABSTRACT FROM AUTHOR]