bluuebunny/crossref_metadata_2025_split huggingface dataset:
Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints
Authors: Deng Shiming , Yano Candace A. 
Published: April 2006

We consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity-constrained manufacturer facing price-sensitive demands. There is a fixed cost per production run and a variable cost per unit produced, both of which may vary by period. We characterize properties of the optimal solution, considering cases with constant and time-varying capacity, and with and without speculative motive for holding inventory. We show that, counter to intuition, optimal prices may increase as the capacity increases, even when capacity is constant over the horizon. We also show that increases in capacity do not always exhibit diminishing marginal returns. Our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well-informed and optimum-seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost. Our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice. Finally, we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem.
The maximum of a random walk whose mean path has a maximum
Authors: Daniels H. E. , Skyrme T. H. R. 
Published: April 2006

This paper discusses the joint distribution of the maximum and the time at which it is attained, of a random walk whose mean path is a curvilinear trend which itself has a maximum. A typical example of such a problem is the distribution of the maximum number of infectives present during the course of an epidemic. Another example where the random walk is constrained to terminate at 0 after a given time is provided by the distribution of the strength and breaking extension of a bundle of fibres.A diffusion approximation to the joint distribution is obtained for the general case of a Brownian bridge. In the commonest class of cases which includes the two examples mentioned, a certain integral equation has to be solved. Its solution enables the marginal distribution of the time to reach the maximum to be tabulated, and the marginal distribution of the maximum confirms the results previously obtained by Daniels (1974) and Barbour (1975). Of particular interest is the conditional expectation of the maximum for a given time of attainment which behaves asymmetrically.
An inventory system for perishable commodities with random lifetime
Authors: Perry David 
Published: April 2006

In this study we assume an inventory system for perishable commodities in which the lifetimes of the items stored are i.i.d. random variable with finite mean.We utilize the analogy between this inventory system and a queueing system with impatient customers, to study the process of the lost demand, the death of the unused items and the number of items in the system.
Asymptotic results for the extinction time of Markov branching processes allowing emigration, I. Random walk decrements
Authors: Pakes Anthony G. 
Published: April 2006

The mathematical model is a Markov branching process which is subjected to catastrophes or large-scale emigration. Catastrophes reduce the population size by independent and identically distributed decrements, and two mechanisms for generating catastrophe epochs are given separate consideration. These are that catastrophes occur at a rate proportional to population size, and as an independent Poisson process.The paper studies some properties of the time to extinction of the modified process in those cases where extinction occurs almost surely. Particular attention is given to limit theorems and the behaviour of the expected extinction time as the initial population size grows. These properties are contrasted with known properties for the case when there is no catastrophe component.
The ages of alleles and a coalescent
Authors: Donnelly Peter , Tavaré Simon 
Published: April 2006

A new coalescent is introduced to study the genealogy of a sample from the infinite-alleles model of population genetics. This coalescent also records the age ordering of alleles in the sample. The distribution of this process is found explicitly for the Moran model, and is shown to be robust for a wide class of reproductive schemes.Properties of the ages themselves and the relationship between ages and class sizes then follow readily.
Recent investigations involving stochastic population models
Authors: Bartlett M. S. 
Published: April 2006

After some introductory general remarks on recent investigations involving population models, two broad classes of stochastic model are discussed further, viz. spatial nearest-neighbour lattice models and doubly stochastic models.In Section 1 of the paper, the first type of model is considered primarily for its relevance to recent work by the author and others affecting the practical design and analysis of replicated field experiments.In Section 2, doubly stochastic processes are discussed more theoretically, particularly models investigated recently by the author involving infinitesimal transition operators in continuous time linear in the (variable) parameters.Some new numerical results on extinction and other ‘absorption' probabilities are presented; these are intended to throw further light on the extent to which the assumption of ‘white-noise' variability of the parameters can be a useful approximation to more realistic models.
Symbolic computation and the diffusion of shapes of triads
Authors: Kendall Wilfrid S. 
Published: April 2006

This paper introduces the use of symbolic computation (also known as computer algebra) in stochastic analysis and particularly in the Itô calculus. Two related examples are considered: the Clifford-Green theorem on random Gaussian triangles, and a generalization of the D. G. Kendall theorem on the kinematics of shape.The Clifford–Green theorem gives a remarkable characterization of the joint distribution of the squared-side-lengths ofnindependent Gaussian points inn-space, namely that this distribution is that ofnindependent exponential random variablesconditionedto satisfy all the inequalities requisite if they are to arise as squared-side-lengths from a point-set inn-space. The D. G. Kendall theorem on the diffusion of shape identifies the statistics of the diffusion arising (under a time-change) as the shape of a triangle whose vertices diffuse by Brownian motion in 2-space or 3-space.Symbolic Itô calculus is used to give a new proof of the Clifford-Green theorem, and to generalize the D. G. Kendall theorem to the case of triangles in higher-dimensional space whose vertices diffuse either according to Brownian motion or according to an Ornstein–Uhlenbeck process.
Asymptotic analysis and computational methods for a class of simple, circuit-switched networks with blocking
Authors: Mitra Debasis 
Published: April 2006

We consider the following circuit-switching problem which is one of the simplest possible extensions of the classical M/M/K/K model: there are p source centers connected to a hub by channels of various line-capacities and the hub is connected to a destination center by a common channel with its own line-capacity. A circuit requires a line from its source to the hub and another line from the hub to the destination. The holding times of circuits are independent, arbitrarily distributed random variables with means which depend on their source, and requests for circuits arrive in Poisson streams. Blocked calls are cleared. The problem is to calculate the blocking probabilities at each of the sources. The formal solution is well known but its calculation is exponentially hard in p.We have developed a technique which extends recent results on integral representations and their asymptotic expansions to obtain the full expansion for the blocking probabilities in inverse powers of a large parameter N. The power of the method derives from two sources: first, an efficient recursive formula for calculating the general term of the expansion; second, tight upper and lower bounds which accompany the estimates. The computational complexity is polynomial in p. We report on computations.
On the stationary waiting-time distribution in theGI/G/1 queue, I: Transform methods and almost-phase-type distributions
Authors: Ott Teunis J. 
Published: April 2006

This paper establishes a link between the Wiener–Hopf factorization and the phase-type method for studying theGI/G/1 queue. Using the Wiener–Hopf factorization, infinite-matrix type results are established for theGI/G/1 queue. An iterative numerical procedure (‘Levinson&s method’) based on these results is described. This method does not always converge. For the situation where either the interarrival times or the service times are of the so-called almost phase type (APH) an alternative, probabilistic derivation of the same results is given. This alternative derivation shows that in the APH situation Levinson&s method converges, converges essentially monotonically, and converges to the correct values.The algorithm has been coded and examples of numerical results are included.
Loss probabilities in a simple circuit-switched network
Authors: Morrison J. A. 
Published: April 2006

In this paper a particular loss network consisting of two links with C1 and C2 circuits, respectively, and two fixed routes, is investigated. A call on route 1 uses a circuit from both links, and a call on route 2 uses a circuit from only the second link. Calls requesting routes 1 and 2 arrive as independent Poisson streams. A call requesting route 1 is blocked and lost if there are no free circuits on either link, and a call requesting route 2 is blocked and lost if there is no free circuit on the second link. Otherwise the call is connected and holds a circuit from each link on its route for the holding period of the call.The case in which the capacities C1, and C2, and the traffic intensities v1, and v2, all become large of O(N) where N » 1, but with their ratios fixed, is considered. The loss probabilities L1 and L2 for calls requesting routes 1 and 2, respectively, are investigated. The asymptotic behavior of L1 and L2 as N→ ∞ is determined with the help of double contour integral representations and saddlepoint approximations. The results differ in various regions of the parameter space (C1, C2, v1, v2). In some of these results the loss probabilities are given in terms of the Erlang loss function, with appropriate arguments, to within an exponentially small relative error. The results provide new information when the loss probabilities are exponentially small in N. This situation is of practical interest, e.g. in cellular systems, and in asynchronous transfer mode networks, where very small loss probabilities are desired.The accuracy of the Erlang fixed-point approximations to the loss probabilities is also investigated. In particular, it is shown that the fixed-point approximation E2 to L2 is inaccurate in a certain region of the parameter space, since L2 « E2 there. On the other hand, in some regions of the parameter space the fixed-point approximations to both L1 and L2 are accurate to within an exponentially small relative error.
A single-server queue with server vacations and a class of non-renewal arrival processes
Authors: Lucantoni David M. , Meier-Hellstern Kathleen S. , Neuts Marcel F. 
Published: April 2006

We study a single-server queue in which the server takes a vacation whenever the system becomes empty. The service and vacation times and the arrival process are all assumed to be mutually independent. The successive service times and the vacation times each form independent, identically distributed sequences with general distributions. A new class of non-renewal arrival processes is introduced. As special cases, it includes the Markov-modulated Poisson process and the superposition of phase-type renewal processes.Algorithmically tractable equations for the distributions of the waiting times at an arbitrary time and at arrivals, as well as for the queue length at an arbitrary time, at arrivals, and at departures are established. Some factorizations, which are known for the case of renewal input, are generalized to this new framework and new factorizations are obtained. The algorithmic implementation of these results is discussed.
Stability of Markovian processes II: continuous-time processes and sampled chains
Authors: Meyn Sean P. , Tweedie R. L. 
Published: April 2006

In this paper we extend the results of Meyn and Tweedie (1992b) from discrete-time parameter to continuous-parameter Markovian processes Φ evolving on a topological space.We consider a number of stability concepts for such processes in terms of the topology of the space, and prove connections between these and standard probabilistic recurrence concepts. We show that these structural results hold for a major class of processes (processes with continuous components) in a manner analogous to discrete-time results, and that complex operations research models such as storage models with state-dependent release rules, or diffusion models such as those with hypoelliptic generators, have this property. Also analogous to discrete time, ‘petite sets', which are known to provide test sets for stability, are here also shown to provide conditions for continuous components to exist.New ergodic theorems for processes with irreducible and countably reducible skeleton chains are derived, and we show that when these conditions do not hold, then the process may be decomposed into an uncountable orbit of skeleton chains.
Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
Authors: Meyn Sean P. , Tweedie R. L. 
Published: April 2006

In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator.Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula.We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion forf-norm convergence, and bounding constants for such convergence in the exponential ergodic case.We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.
Random motions governed by third-order equations
Authors: Orsingher Enzo 
Published: April 2006

In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation.We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process.Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.
The asymptotic behaviour of extinction probability in the Smith–Wilkinson branching process
Authors: Grey D. R. , Zhunwei Lu 
Published: April 2006

Under some regularity conditions, in the supercritical Smith–Wilkinson branching process it is shown that as k, the starting population size, tends to infinity, the rate of convergence of qk, the corresponding extinction probability, to zero is similar to that of:k–θ, if there exists at least one subcritical state in the random environment space; xkk–α, if there exist only supercritical states in the random environment space; exp , if there exists at least one critical state and the others are supercritical in the random environment space.Here θ, x, α and c are positive constants determined by the process.
Customer routing to different servers with complete information
Authors: Rosberg Zvi , Kermani Parviz 
Published: April 2006

In this paper we consider a queueing system having n exponential servers, each with its own queue and service rate. Customers arrive according to a Poisson process with rate λ, and upon arrival each customer must be routed to some server's queue. No jockeying amongst the queues is allowed and each server serves its queue according to a first-come-first-served discipline.Each server i, 1 ≦ i ≦ n, provides service with a state-dependent rate μ(i)(k), k = 0, 1, …. In addition, at every queue i, there is a deterministic holding cost which occurs at rate h(i)(k) while there are k customers at the queue.An admissible routing policy is a policy that assigns each arriving customer to one of the queues. A decision at time t may be randomized and dependent on the queue lengths and decisions till time t. An optimal routing policy is an admissible policy that minimizes the long-run average holding cost.In this study, we bound the optimal cost from below, by considering an ideal system, where each server optimally selects a given proportion of customers, irrespective of other servers' selections. From this ideal system we construct a class of admissible routing policies, the overflow routing class, that approximates the ideal situation for each server. Finally, we evaluate the policies and compare them to the lower bound.
Explosive Markov branching processes: entrance laws and limiting behaviour
Authors: Pakes Anthony G. 
Published: April 2006

The supercritical Markov branching process is examined in the case where the minimal version of the process has strictly substochastic transition laws. This provides a nice example of the general construction theory for discrete-state Markov processes.Entrance laws corresponding to the minimal process are characterised. Limit properties of the processes constructed from these entrance laws are examined. All such processes which are honest and cannot hit zero are ergodic. Otherwise these processes are λ-positive and limit theorems conditional on not having left the positive states are given.A connection is made with recent work on the general construction problem when a λ-subinvariant measure is given. The case where immigration is allowed is mentioned.
General optimal stopping theorems for semi-Markov processes
Authors: Boshuizen Frans A. , Gouweleeuw José M. 
Published: April 2006

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made.Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases.The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].
Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state
Authors: Pakes Anthony G. 
Published: April 2006

Under consideration is a continuous-time Markov process with non-negative integer state space and a single absorbing state 0. Let T be the hitting time of zero and suppose Pi(T < ∞) ≡ 1 and (*) limi→∞Pi(T > t) = 1 for all t > 0. Most known cases satisfy (*). The Markov process has a quasi-stationary distribution iff Ei (e∊T) < ∞ for some ∊ > 0.The published proof of this fact makes crucial use of (*). By means of examples it is shown that (*) can be violated in quite drastic ways without destroying the existence of a quasi-stationary distribution.
Analysis of an M/G/1 queue with two types of impatient units
Authors: Martin M. , Artalejo J. R. 
Published: April 2006

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later.We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.
Delays to road traffic at an intersection
Authors: Yeo G. F. , Weesakul B. 
Published: April 2006

A model for road traffic delays at intersections is considered where vehicles arriving, possibly in bunches, in a Poisson process in a one way minor road yield right of way to traffic, which forms alternate bunches and gaps, in a major road. The gap acceptance times are random variables, and depend on whether or not a minor road vehicle is immediately following another minor road vehicle into the intersection or not.The transforms of the stationary waiting time and queue size distributions, and the mean stationary delay, for minor road vehicles are obtained by substitution of determined service time distributions into results for a generalisation of theM/G/1 queueing system. Some numerical results are given to illustrate the increase in the mean delay for variable gap acceptance times for a Borel-Tanner distribution of major road traffic, and a partial solution is given for a two way major road.
Incomplete discontinuous Markov processes
Authors: Moyal J. E. 
Published: April 2006

SummaryThe present paper generalizes the results of the author's paper [2] on “Discontinuous Markov processes” to processes that are incompletely specified. These results are then used to develop a step-by-step method of solution for processes involving several kinds of “jumps”, where at the first step one solves for the transition probabilities involving jumps of the first kind, but not of the second, third, etc., at the second step for transition probabilities involving jumps of the first and second, but not the third, fourth, etc. kinds, and so on. Some examples are given.
On infinite server queues with batch arrivals
Authors: Shanbhag D. N. 
Published: April 2006

The queueing system studied in this paper is the one in which(i)there are an infinite number of servers,(ii)initially (att= 0) all the servers are idle,(iii)one server serves only one customer at a time and the service times are independent and identically distributed with distribution functionB(t) (t> 0) and mean β(< ∞),(iv)the arrivals are in batches such that a batch arrives during (t,t+ δt) with probability λ(t)δt+o(δt) (λ(t) > 0) and no arrival takes place during (t,t+ δt) with the probability 1 –λ(t)δt+o(δt),(v)the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given byar(r≧ 1),(vi)the batch sizes, the service times and the arrivals are independent.