Optimal multithreshold control for a BMAP/G/1 queue with N service modes

Evolutionary systems are used for search and optimization in complex problems and for modelling population dynamics in nature. Individuals in populations reproduce by simple mechanisms, such as mutation or recombination of their genetic sequences, and selection ensures they evolve in the direction of increasing fitness. Although successful in many applications, evolution towards an optimum or high fitness can be extremely slow, and the problem of controlling parameters of reproduction to speed up this process has been investigated by many researchers. Here, we approach the problem from two points of view: (1) as optimization of evolution in time; (2) as optimization of evolution in information. The former problem is often intractable, because analytical solutions are not available. The latter problem, on the other hand, can be solved using convex analysis, and the resulting control, optimal in the sense of information dynamics, can achieve good results also in the sense of time evolution. The principle is demonstrated on the problem of optimal mutation rate control in Hamming spaces of sequences. To facilitate the analysis, we introduce the notion of a relatively monotonic fitness landscape and obtain general formula for transition probability by simple mutation in a Hamming space. Several rules for optimal control of mutation are presented, and the resulting dynamics are compared and discussed.

In this paper, we consider a single server queuing model with an infinite buffer in which customers arrive according to a batch Markovian arrival process (BMAP). The services are offered in two modes. In mode 1, the customers are served one at a time and in mode 2 customers are served in groups of varying sizes. Various costs for holding, service and switching are imposed. For a given hysteretic strategy, we derive an expression for the cost function from which an optimal hysteretic control can be obtained. Illustrative numerical examples are presented.

We investigate the problem of optimal control of mutation by asexual self-replicating organisms represented by points in a metric space. We introduce the notion of a relatively monotonic fitness landscape and consider a generalisation of Fisher’s geometric model of adaptation for such spaces. Using a Hamming space as a prime example, we derive the probability of adaptation as a function of reproduction parameters (e.g. mutation size or rate). Optimal control rules for the parameters are derived explicitly for some relatively monotonic landscapes, and then a general information-based heuristic is introduced. We then evaluate our theoretical control functions against optimal mutation functions evolved from a random population of functions using a meta genetic algorithm. Our experimental results show a close match between theory and experiment. We demonstrate this result both in artificial fitness landscapes, defined by a Hamming distance, and a natural landscape, where fitness is defined by a DNA-protein affinity. We discuss how a control of mutation rate could occur and evolve in natural organisms. We also outline future directions of this work.

The paper considers a classical M/M/1 queue with two priority classes under a preemptive priority discipline. Based on the performance measures of White and Christie [14], the paper studies the optimal pricing policy of the server who is an individual profit maximizer when the customers adopt their respective equilibrium arrival rate, then discusses the service rate control problem from the perspective of social welfare maximization. Because of the complexity of the model, it's intractable to theoretically analyze the queueing system in depth. In the section of example analyses, two numerical examples are presented, on the one hand to give the specifically optimal pricing policy and service rate control policy, and on the other hand to conduct some sensitivity analyses for some important parameters.

We propose a novel recursive algorithm for determining the optimal admission and transmission rates for an M/M/1 transmitter buffer for obtaining minimum average queue length, under quasi-static fading, while satisfying a throughput constraint with given available transmit power. The optimal rate setting policy is obtained with significant savings in memory and computational complexity, and is simple and easy to implement.

A sufficient condition for a BMAP/M/N system to have a stationary state probability distribution and an algorithm for computing this distribution are investigated.

In this paper, we study cross-layer design for rate control in multihop wireless networks. In our previous work, we have developed an optimal cross-layered rate control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal cross-layered rate control scheme has to solve a complex global optimization problem at each time, and hence is too computationally expensive for online implementation. In this paper, we study how the performance of cross-layer rate control can be impacted if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study both the case when the number of users in the system is fixed and the case with dynamic arrivals and departures of the users, and we establish desirable results on the performance bounds of cross-layered rate control with imperfect scheduling. Compared with a layered approach that does not design rate control and scheduling together, our cross-layered approach has provably better performance bounds, and substantially outperforms the layered approach. The insights drawn from our analyses also enable us to design a fully distributed cross-layered rate control and scheduling algorithm for a restrictive interference model.

Funding AcknowledgementsType of funding sources: Public grant(s) – National budget only. Main funding source(s): Netherlands Organization for Health Research and DevelopmentIntroductionIn the Rate Control versus Electrical Cardioversion Trial 7–Acute Cardioversion versus Wait and See, patients with recent-onset atrial fibrillation (AF) were randomised to either early or delayed cardioversion.PurposeThis pre-specified sub-analysis aimed to evaluate heart rate during AF recurrences after an emergency department (ED) visit identified by an electrocardiogram (ECG)-based handheld device.MethodsAfter the ED visit, included patients (n=437) were asked to use an ECG-based handheld device to monitor for recurrences during the four-week follow-up period. 335 patients used the handheld device and were included in this analysis. Recordings from the device were collected and assessed for heart rhythm and rate. Optimal rate control was defined as a target resting heart rate of <110 bpm.ResultsIn 99 patients (29.6%, mean age 67±10 years, 39.4% female, median 6 [3-12] AF recordings) a total of 314 AF recurrences (median 2 [1-3] per patient) were identified during the follow-up. The average median resting heart rate at recurrence was 100±21 bpm in the delayed vs 112±25 bpm in the early cardioversion group (p=0.011). Additionally, the maximum heart rate was also significantly lower in the delayed cardioversion group (115 [94-131] vs 136 [118-147], p=0.001). Optimal rate control was seen in 68.4% [21.3-100%] of the performed recordings per patient in the delayed, and 33.3% [0-77.5%] of the performed recordings per patient in the early cardioversion group (p=0.01). Randomisation group (coefficient -12.09 (-20.55 - -3.63, p=0.006) for delayed versus early cardioversion) and heart rate on index ECG (coefficient 0.46 (0.29-0.63, p<0.001) per bpm increase) were identified as multivariable adjusted factors associated with lower median heart rate during AF recurrences.ConclusionA delayed cardioversion strategy translated into lower median heart rates as well as lower peak heart rates during AF recurrences. Apart from the randomized treatment, heart rate at recurrence was influenced by the intrinsic heart rate on presentation.

A tandem retrial queueing system with two Markovian flows and reservation of channels

In optimal control loops delays can occur, for example through transmission via digital communication channels. Such delays influence the state that is generated by the implemented control. We study the effect of a delay in the implementation of L2-norm minimal Neumann boundary controls for the wave equation. The optimal controls are computed as solutions of problems of exact optimal control, that is if they are implemented without delay, they steer the system to a position of rest in a given finite time T. We show that arbitrarily small delays δ> 0 can have a destabilizing effect in the sense that we can find initial states such that if the optimal control u is implemented in the form yx(t,1) = u(t − δ) for t>δ, the energy of the system state at the terminal time T is almost twice as big as the initial energy. We also show that for more regular initial states, the effect of a delay in the implementation of the optimal control is bounded above in the sense that for initial positions with derivatives of BV-regularity and initial velocities with BV-regularity, the terminal energy is bounded above by the delay δ multiplied with a factor that depends on the BV-norm of the initial data. We show that for more general hyperbolic optimal exact control problems the situation is similar. For systems that have arbitrarily large eigenvalues, we can find terminal times T and arbitrarily small time delays δ, such that at the time T + δ, in the optimal control loop with delay the norm of the state is twice as large as the corresponding norm for the initial state. Moreover, if the initial state satisfies an additional regularity condition, there is an upper bound for the effect of time delay of the order of the delay with a constant that depends on the initial state only.

Concerns the question whether it be possible to find infinitesimal conditions characterizing optimal feedback control in problems of control under disturbance and differential games which are analogous to Pontryagin minimum principle in optimal control. The positive answer to this question is given in terms of some minimum principles in integral and pointwise forms for optimal feedback. The derivation of pointwise minimum principle from integral one requires special technique based on the theorem on disintegration of measure. This technique which is especially suited for the consideration of nonanticipating strategies is applied to the construction of the duality theory for linear-convex differential games. We discuss here the application of the pointwise minimum principle to the solution of the long standing problem of optimality of some natural pursuit strategy in the game problem Lion and Man of Rado (1928). >

SummaryThe problem of adaptive optimal semiactive control of a structure subjected to a moving load is studied. The control is realised by a change of damping of the structure's supports. The results presented in the previous works of the authors demonstrate that switched optimal controls can be very efficient at reducing the vibration levels of the structure. On the other hand, these controls exhibit a high sensitivity to changes of the speed of the travelling load. The aim of this paper is to develop an algorithm that enables real‐time adaptation of the optimal controls according to both the measured speed of the travelling load and the estimated state of the structure. The control objective is to provide smooth passage for the vehicles and reduce the material stresses on the carrying structures. The designed adaptive algorithm uses reference optimal controls computed for constant speeds and a set of functions describing the sensitivity of the system dynamics to the measured parameters. The convergence of the algorithm, as well as aspects of its implementation, is studied. The performance of the proposed method is validated by means of numerical simulations conducted for different travelling speed scenarios. In the assumed objective functional, the proposed adaptive controller can outperform the reference optimal solutions by over 50%. The practicality of the proposed method should attract the attention of practising engineers.

Consider a wireless networking architecture, where multiple infrastructure access points (AP) dynamically offer (bid) service deals (modes) to a mobile over time. Akin to a market offer, each service deal is comprised of service/quality attributes (e.g, AP, rate) for a price (cost). The mobile dynamically selects the desirable deal at each time, so as to efficiently trade long term latency/quality for cumulative price. Offered service modes depend on the randomly fluctuating congestion state of the AP infrastructure. Dynamically switching from one service mode/deal to another, the mobile encounters `friction' (e.g. bandwidth loss, disconnection risk) and, hence, has an incentive to stick with the current deal for as long as this is significantly competitive. A model of this architecture is first developed, which allows for the formulation and computation of the optimal control for the mobile to accept an offered deal amongst many and switch into the corresponding service mode. A suite of low-complexity heuristic controls for mode switching is also discussed. The performance of the optimal and heuristic controls is probed via simulation. Finally, the `switching curve' structure of the optimal control is demonstrated on a simple system where the curves can be plotted.

We consider the problem of joint service rate control and load balancing of a network of servers. The system incurs holding cost, effort cost, and a routing cost whenever a demand is routed to other servers. This formulation is motivated by recent interest on energy efficiency in IT systems where effort cost models power consumption and holding cost represents performance in terms of delay. The aim is to find a stationary policy that minimizes, over an infinite horizon, the long-run average cost rate. Using a dynamic programming formulation, we show that the optimal routing policy is acyclic and bipartite. We prove that the relative cost function is monotonically non-decreasing in queue size while for the case of 2 servers, the optimal service policy is non-decreasing in queue size and the optimal routing policy is a threshold policy. We show how upper and lower bounds of the optimal average cost rate can be efficiently calculated numerically. In particular, based on the monotonicity property, we develop an approximate dynamic programming procedure to efficiently compute a good upper bound. Numerical examples with two networked servers are provided to illustrate our findings.

In this paper, we consider the problem of rate control for video transmission over variable bit rate (VBR) channels. We focus on finding off-line optimal rate control for VBR transmission with a token bucket policing function. To ensure a maximum minimum quality is obtained over all data units, we introduce a minimum maximum distortion (MMAX) criterion in this channel-constrained problem. We show that, due to the channel constraints, a MMAX solution leads to a relatively low average distortion, because the total rate budget is not completely utilized. Therefore, after finding a MMAX solution, an additional minimization of average distortion (MMAX+) criterion is proposed to increase overall quality of the data sequence by using remaining resources. The proposed algorithms lead to an increase in average quality with respect to the MMAX solution, while providing a much more constant quality than MMSE solutions. Moreover we show how the MMAX+ approach can be implemented with low complexity.