comparisons between observable and unobservable m m 1 queues with respect to optimal customer behavior we consider an m m 1 queueing system in which the queue length may or may not be observable by a customer upon entering the system the observable and unobservable models are compared with respect to system properties and performance measures under two different types of optimal customer behavior which we refer to as selfishly optimal and socially optimal we consider average customer throughput rates and show that under both types of optimal customer behavior the equality of effective queue joining rates between the observable and unobservable systems results in differences with respect to other performance measures such as mean busy periods and waiting times we also show that the equality of selfishly optimal queue joining rates between the two types of system precludes the equality of socially optimal joining rates and vice versa

riemann cartan geometry of nonlinear dislocation mechanics we present a geometric theory of nonlinear solids with distributed dislocations in this theory the material manifold where the body is stress free is a weitzenbock manifold that is a manifold with a flat affine connection with torsion but vanishing non metricity torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics using cartan s moving frames we construct the material manifold for several examples of bodies with distributed dislocations we also present non trivial examples of zero stress dislocation distributions more importantly in this geometric framework we are able to calculate the residual stress fields assuming that the nonlinear elastic body is incompressible we derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

involutive systems of differential equations einstein s strength versus cartan s degre d arbitraire three new theorems relating einstein s notions of strength and compatibility to the field of the initial value problem are presented these theorems result i in a first proof of matthews conjectures concerning this relation for a wider class of systems of partial differential equations ii in a new interpretation of einstein s compatibility condition and iii in the exact relation between einstein s strength and cartan s degre d arbitraire

lagrange multipliers and gauss bonnet type invariants in riemann cartan space a lagrange multiplier approach is applied to gauss bonnet type invariants in riemann cartan geometry lanczos type identities are then derived the use of the variational procedure in the context of gravitational theories with a gauss bonnet invariant limit is discussed

asymptotic feedback stabilization a sufficient condition for the existence of control lyapunov functions abstract in this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control we offer sufficient conditions for the existence of control lyapunov functions that according to 3 23 and 28 30 guarantee stabilization at a specified equilibrium by means of a feedback law which is smooth except possibly at the equilibrium we note that the results of the paper present a local nature

hybrid queueing systems with hysteretic bilevel control policies abstract this article analyzes a stochastic hybrid system with compound poisson input general batch service and two vacation modes that operate in accordance with a so called bilevel hysteretic control in the context of queues with vacations most stochastic systems function either under multiple or single vacation regimes and they are initiated whenever the queue length becomes zero in this model we combine the two modes in one hybrid system that switches to a multiple or single vacation modes which consists of multiple or single segments respectively whenever the queue drops below some r 1 or falls into r 1 r 2 upon the end of a service the servicing facility then assumes some other activities the main service is restored when the queue length reaches or exceeds some n r 2 upon the completion of a vacation segment we use fluctuation analysis and semi regenerative techniques to arrive at closed form functionals for the steady state probabilities of queueing processes both for discrete and for continuous time parameter processes and discuss special cases to demonstrate the applicability of the results the latter can potentially be used to optimize the system with respect to parameters r 1 r 2 and n

a simple characterization of optimal arma predictors abstract the coefficients of the optimal steady state k step ahead predictor for an arma process in general depend on k it is shown that a simple formula completely characterizes all these coefficients

on the linear quadratic guassian problem with correlated noise and its relation to minimum variance control the linear quadratic gaussian log stochastic control problem with correlated dynamic and observation noise and no information delay is studied an explicit feedback solution is given for finite as well as infinite time problems these results are then applied to minimum variance control of single input single output armax systems the lqg controller and the minimum variance controller obtained using input output methods are shown to be identical for any system delay extending a result of 5

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

optimal policies of m t m c c queues with two different levels of servers abstract this paper deals with optimal control points of m t m c c queues with periodic arrival rates and two levels of the number of servers we use the results of this model to build a markov decision process mdp the problem arose from a case study in the kelowna general hospital kgh the kgh uses surge beds when the emergency room is overcrowded which results in having two levels for the number of the beds the objective is to minimize a cost function the findings of this work are not limited to the healthcare they may be used in any stochastic system with fluctuation in arrival rates and or two levels of the number of servers i e call centers transportation and internet services we model the situation and define a cost function which needs to be minimized in order to find the cost function we need transient solutions of the m t m c c queue we modify the fourth order runge kutta to calculate the transient solutions and we obtain better solutions than the existing runge kutta method we show that the periodic variation of arrival rates makes the control policies time dependent and periodic we also study how fast the policies converge to a periodic pattern and obtain a criterion for independence of policies in two sequential cycles

an identity in riemann cartan geometry we derive a new gauss bonnet type identity in riemann cartan geometry g 1 2e r 1 2 c c g 1 2e c where c is the torsion tensor

inefficiency of nash equilibria it is shown that nash equilibria of smooth games generally tend to be inefficient in the pareto sense

individual versus social optimization in the allocation of customers to alternative servers customers arrive at a service area according to a poisson process an arriving customer must choose one of k servers without observing present congestion levels the only available information about the kth server is the service time distribution with expected duration k 1 and the cost per unit time of waiting at the kth server hk although service distributions may differ from server to server and need not be exponential it is assumed that they share the same coefficient of variation individuals acting in self interest induce an arrival rate pattern 1 2 k in contrast the social optimum is the arrival rate pattern 1 2 k which minimizes long run average cost per unit time for the entire system the main result is that k s and k s differ systematically individuals overload the servers with the smallest hk k values for an exponential service case with pre emptive lifo service an alternative charging scheme is presented which confirms that differences between individual and social optima occur precisely because individuals fail to consider the inconvenience that they cause to others

underdetermined systems of partial differential equations this paper examines underdetermined systems of partial differential equations in which the independent variables may be classical c numbers or even quantum operators one can view an underdetermined system as expressing the kinematic constraints on a set of dynamical variables that generate a lie algebra the arbitrariness in the general solution reflects the freedom to specify the dynamics of such a system

global stabilizability of homogeneous vector fields of odd degree abstract in this paper we deal with global stabilizability at the origin of a homogeneous vector field by means of homogeneous feedbacks of the same degree we give a sufficient condition which turns out to be also necessary in the linear case for a particular class of systems this condition is implied by a local controllability assumption

chern simons terms in metric affine space time bianchi identities as euler lagrange equations the metric affine gauge theory of gravity encompasses a space time with the following geometrical fields coframe metric g and an independent linear connection within this geometrical framework all four forms b dc are constructed which qualify as boundary terms for a gauge lagrangian that is they are gl 4 r scalars as well as exact forms derived from chern simons type three forms c the result of our search is summarized in eq 4 20 the translational piece dctt is new the boundary terms effectively serve as lagrangians for the bianchi identities of nonmetricity torsion and curvature in the canonical formalism the normal parts of the chern simons three forms represent generating functions that are capable of generating new ashtekar type variables eventually the bach lanczos identity is generalized to the metric affine space time

magnitude of inefficiency abstract various types of inefficiencies of a system state like the nash equilibrium ne exist such as social inefficiency pareto inefficiency etc a system state is inefficient if it is inferior to another realizable state firstly this article presents a general procedure to obtain each inefficiency measure the procedure brings as each inefficiency measure the maximum degree of corresponding inferiority of the state to some other we examine the procedure in the game theory context vastly many people use the social inefficiency measure represented by the price of anarchy poa however it cannot always serve as a pareto inefficiency measure contrarily the pareto inefficiency measures are yet to establish secondly we follow the procedure to which poa also conforms and obtain pareto inefficiency measures we confirm that they distinguish pareto inefficiencies that poa cannot always distinguish we show a fixed relation between the values of the measures further if a state is proportional to a pareto optimal state proposed measures of strict pareto inefficiency and pareto inefficiency behave in identical and straightforward ways then their value is the proportionality constant using examples we examine the measures

invariant variational problems on linear frame bundles the hamiltonian structure of variational problems defined by the natural basis jki of diff m invariant lagrangians on the 1 jet bundle of linear frames of a m dimensional manifold m is described diffeomorphism invariance on j1 fm and its infinitesimal counterpart i e invariance under the natural representation of vector fields of m are analysed the lagrangians jki are proved to be the basic tools required to factor diff m g invariance into diff m invariance and g invariance the densities jki jki 1 m where the i are the components of the canonical form are shown to define two types of variational problem according to whether i j k or i j k the field equations for their extremals are deduced these equations are examples of underdetermined non linear systems of partial differential equations extremals defining a lie algebra structure are characterized the functions in the real linear space spanned by jki are the only lagrangians on fm admitting a hamiltonian formalism of order zero infinitesimal symmetries and noether invariants of the densities jki are studied in detail in particular it is proved that the noether invariant of every vertical symmetry vanishes hence only the horizontal symmetries appear in the hamiltonian structure the equations of the jacobi fields along an extremal are explicitly obtained the pre symplectic structure attached to jki is defined to be an alternate bilinear map 2 s on the space of jacobi fields along an extremal s with values in closed m 1 forms on m and its kernel is related to vertical infinitesimal symmetries of the lagrangian for m 3 4 the equations of the extremals are integrated explicitly we thus obtain normal forms which when transformed by an arbitrary diffeomorphism yield the general solution to the field equations

problems with metric teleparallel theories of gravitation a general lagrangian formulation of the metric affine metric compatible theories of gravitation is given the applicability of the metric teleparallel geometry to gravitation is considered it is pointed out that a teleparallel theory with the lagrangian usually accepted in the literature leads to a non predictable behaviour of torsion a new choice of the lagrangian is proposed

customer equilibrium and optimal strategies in an m m 1 queue with dynamic service control abstract we consider the problem of customer equilibrium strategies in an m m 1 queue under dynamic service control the service rate switches between a low and a high value depending on system congestion arriving customers do not observe the system state at the moment of arrival we show that due to service rate variation the customer equilibrium strategy is not generally unique and derive an upper bound on the number of possible equilibria for the problem of social welfare optimization we numerically analyze the relationship between the optimal and equilibrium arrival rates as a function of various parameter values and assess the level of inefficiency via the price of anarchy measure we finally derive analytic solutions for the special case where the service rate switch occurs when the queue ceases to be empty

the pointwise stationary approximation for queues with nonstationary arrivals we empirically explore the accuracy of an easily computed approximation for long run average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic sinusoidal poisson arrival processes the pointwise stationary approximation is computed by integrating over time that is taking the expectation of the formula for the stationary performance measure with the arrival rate that applies at each point in time this approximation which has been empirically confirmed as a tight upper bound of the true value is shown to be very accurate for a range of parameter values corresponding to a reasonably broad spectrum of real systems