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We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a continuous-time version of these processes, called total-progeny-dependent birth-and-death processes, and study some of their properties through the analysis of their deterministic (fluid) approximation. These properties include the maximum population size, the total progeny size at extinction, the time to reach the maximum population size, and the time until extinction. As the fluid approximation does not allow us to determine the time until extinction directly, we propose several methods to complement this approach. We also use the deterministic approach to study the behavior of the processes as we increase the magnitude of the individual's birth rate. [ABSTRACT FROM AUTHOR]

In this paper we introduce new birth-and-death processes with partial catastrophe and study some of their properties. In particular, we obtain some estimates for the mean catastrophe time, and the first and second moments of the distribution of the process at a fixed time t. This is completed by some asymptotic results. [ABSTRACT FROM AUTHOR]

Mobile edge computing (MEC) is one of the key technologies to achieve high bandwidth, low latency and reliable service in fifth generation (5G) networks. In order to better evaluate the performance of the probabilistic offloading strategy in a MEC system, we give a modeling method to capture the stochastic behavior of tasks based on a multi-source fluid queue. Considering multiple mobile devices (MDs) in a MEC system, we build a multi-source fluid queue to model the tasks offloaded to the MEC server. We give an approach to analyze the fluid queue driven by multiple independent heterogeneous finite-state birth-and-death processes (BDPs) and present the cumulative distribution function (CDF) of the edge buffer content. Then, we evaluate the performance measures in terms of the utilization of the MEC server, the expected edge buffer content and the average response time of a task. Finally, we provide numerical results with some analysis to illustrate the feasibility of the stochastic model built in this paper.

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process conditioned upon never being absorbed. The technique relies on a coupling procedure that is related to Harris recurrence (for Markov Chains). It applies to general continuous-time and continuous-space Markov processes. The main novelty is that we modulate each coupling step depending both on a final horizon of time (for survival) and on the initial distribution. By this way, we could notably include in the convergence a dependency on the initial condition. As an illustration, we consider a continuous-time birth–death process with catastrophes and a diffusion process describing a (localized) population adapting to its environment. [ABSTRACT FROM AUTHOR]

A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Pólya urn model with removals. [ABSTRACT FROM AUTHOR]

Recently, the asymptotic mean value of the height for a birth-and-death process is given in Videla [Videla, L.A. (2020)]. We consider the asymptotic variance of the height in the case when the number of states tends to infinity. Further, we prove that the heights exhibit a cutoff phenomenon and that the normalized height converges to a degenerate distribution. [ABSTRACT FROM AUTHOR]

Mobile edge computing (MEC) is one of the key technologies to achieve high bandwidth, low latency and reliable service in fifth generation (5G) networks. In order to better evaluate the performance of the probabilistic offloading strategy in a MEC system, we give a modeling method to capture the stochastic behavior of tasks based on a multi-source fluid queue. Considering multiple mobile devices (MDs) in a MEC system, we build a multi-source fluid queue to model the tasks offloaded to theMEC server. We give an approach to analyze the fluid queue driven by multiple independent heterogeneous finite-state birth-and-death processes (BDPs) and present the cumulative distribution function (CDF) of the edge buffer content. Then, we evaluate the performance measures in terms of the utilization of the MEC server, the expected edge buffer content and the average response time of a task. Finally, we provide numerical results with some analysis to illustrate the feasibility of the stochastic model built in this paper. [ABSTRACT FROM AUTHOR]

We provide new necessary and sufficient conditions for the convergence of positive series developing Bertran-De Morgan and Cauchy type tests given in [M. Martin, Bull. Amer. Math. Soc. 47(1941), 452-457] and [L. Bourchtein et al, Int. J. Math. Anal. 6(2012), 1847-1869]. The obtained result enables us to extend the known conditions for recurrence and transience of birth-and-death processes given in [V. M. Abramov, Amer. Math. Monthly 127(2020) 444-448]. [ABSTRACT FROM AUTHOR]

Independent origins of sociality in bees and ants are associated with independent expansions of particular odorant receptor (OR) gene subfamilies. In ants, one clade within the OR gene family, the 9-exon subfamily, has dramatically expanded. These receptors detect cuticular hydrocarbons (CHCs), key social signaling molecules in insects. It is unclear to what extent 9-exon OR subfamily expansion is associated with the independent evolution of sociality across Hymenoptera, warranting studies of taxa with independently derived social behavior. Here, we describe OR gene family evolution in the northern paper wasp, Polistes fuscatus , and compare it to four additional paper wasp species spanning ∼40 million years of evolutionary divergence. We find 200 putatively functional OR genes in P. fuscatus , matching predictions from neuroanatomy, and more than half of these are in the 9-exon subfamily. Most OR gene expansions are tandemly arrayed at orthologous loci in Polistes genomes, and microsynteny analysis shows species-specific gain and loss of 9-exon ORs within tandem arrays. There is evidence of episodic positive diversifying selection shaping ORs in expanded subfamilies. Values of omega (d N/ d S) are higher among 9-exon ORs compared to other OR subfamilies. Within the Polistes OR gene tree, branches in the 9-exon OR clade experience relaxed negative (relaxed purifying) selection relative to other branches in the tree. Patterns of OR evolution within Polistes are consistent with 9-exon OR function in CHC perception by combinatorial coding, with both natural selection and neutral drift contributing to interspecies differences in gene copy number and sequence. [ABSTRACT FROM AUTHOR]

In this paper a novelty Massive Multiple Input Multiple Output (MIMO) channel model based on the birth‐and‐death process of multipath clusters is proposed. First, Massive MIMO measurements are conducted in typical outdoSor scenarios with the bandwidth of 100 MHz at frequencies of 1.4725 and 6 GHz, respectively, following with the investigation of radio propagation characteristics over antenna array. Then we research on the subchannel correlation and nonstationary based on the channel sounding experiments. Furthermore, we build up a Markov chain to characterize the birth‐and‐death process of the multipath clusters over the array, which is helpful to bring deeply insight into the cluster evolution over the antenna array axis. And the analysis results are consistent with the theory of the cluster's visible region. At last, the paper systematically demonstrates how does the spatial correlation influence the capacity of the communication system. The whole research work aims to contribute the radio channel modeling of the fifth‐generation (5G) Massive MIMO communication system. Key Points: Wideband multiantenna measurements are taken for Massive MIMO channelsCluster's birth‐and‐death process over the antenna array is studied to characterize nonstationary of Massive MIMO channelChannel capacity is studied to have an insight into the degradation caused by antenna correlation [ABSTRACT FROM AUTHOR]

Two problems in population dynamics are addressed in a slow or rapid periodic environment. We first obtain a Taylor expansion for the probability of non-extinction of a supercriticial linear birth-and-death process with periodic coefficients when the period is large or small. If the birth rate is lower than the mortality for part of the period and the period tends to infinity, then the probability of non-extinction tends to a discontinuous limit related to a "canard" in a slow-fast system. Secondly, a nonlinear S-I-R epidemic model is studied when the contact rate fluctuates rapidly. The final size of the epidemic is close to that obtained by replacing the contact rate with its average. An approximation of the correction can be calculated analytically when the basic reproduction number of the epidemic is close to 1. The correction term, which can be either positive or negative, is proportional to both the period of oscillations and the initial fraction of infected people. [ABSTRACT FROM AUTHOR]

We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the classical birth-and-death process with immigration of Karlin and McGregor (1967), in turn related to the celebrated Ewens sampling formula. A biological basis for the scheme is provided in terms of a population of individuals grouped into families, that evolves according to a sequence of births, deaths and immigrations. We investigate the asymptotic behaviour of the chain and show that, as opposed to the birth-and-death process with immigration, this construction maintains in the temporal limit the mutual dependence among the multiplicities. When the death rate exceeds the birth rate the system is shown to have a reversible distribution, identified as a mixture of Pitman sampling formulae, with negative binomial mixing distribution on the population size. The population therefore converges to a stationary random configuration, characterised by a finite number of families and individuals. [ABSTRACT FROM AUTHOR]

In this paper, we consider discrete growth–decay–fragmentation equations that describe the size distribution of clusters that can undergo splitting, growth and decay. The clusters can be for instance animal groups that can split but can also grow, or decrease in size due to birth or death of individuals in the group, or chemical particles where the growth and decay can be due to surface deposition or erosion. We prove that for a large class of such problems, the solution semigroup is analytic and compact and thus has the asynchronous exponential growth property; that is, the long-term behaviour of any solution is given by a scalar exponential function multiplied by a vector, called the stable population distribution, that is independent on the initial conditions. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the long-term behaviour of a continuous-time Markov chain that can be interpreted as a pair of linear birth processes which evolve with a competitive interaction; as a special case, they include the famous Lotka–Volterra interaction. Another example of our process is related to urn models with ball removal. We show that, with probability one, the process eventually escapes to infinity by sticking to the boundary in a rather unusual way. [ABSTRACT FROM AUTHOR]

Consider a queueing network with a large number N nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the M / M / 1 queue with a modified arrival rate when the queue length is around zero. [ABSTRACT FROM AUTHOR]

We consider an M/M/m preemptive-resume last-come first-served (PR-LCFS) queue without exogenous priority classes of impatient customers. We focus on analyzing the time interval from the arrival to either service completion or abandonment for an arbitrary customer. We formulate the problem as a one-dimensional birth-and-death process with two absorbing states, and consider the first passage times in this process. We give explicit expressions for the probabilities of service completion and abandonment. Furthermore, we present sets of recursive computational formulas for calculating the mean and second moment of the times until service completion and abandonment. The two special cases of a preemptive-loss system and an ordinary M/M/m queue with patient customers only, both incorporating the preemptive LCFS discipline, are treated separately. We show some numerical examples in order to demonstrate the computation of theoretical formulas. [ABSTRACT FROM AUTHOR]

In the present paper, we define conservative and semiconservative random walks in Zd and study various families of random walks. The family of symmetric random walks is one of the families of conservative random walks, and simple (Pólya) random walks are their representatives. The classification of random walks given in the present paper enables us to provide a new approach to random walks in Zd by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in Zd for any d≥3 and transient random walks in Z2. [ABSTRACT FROM AUTHOR]

We consider the distribution of the age of an individual picked uniformly at random at some fixed time in a linear birth-and-death process. By exploiting a bijection between the birth-and-death tree and a contour process, we derive the cumulative distribution function for this distribution. In the critical and supercritical cases, we also give rates for the convergence in terms of the total variation and other metrics towards the appropriate exponential distribution. [ABSTRACT FROM AUTHOR]

We consider the problems of developing hybrid wireless systems based on laser and radio technologies. We present a new method for estimating the characteristics of such systems operating in a random semi-Markov environment. The method is based on the theory of Markov modulated processes. We develop an efficient algorithm for computing the stationary probability distribution of the states and performance characteristics for hybrid systems. A numerical example illustrates the proposed approach. [ABSTRACT FROM AUTHOR]

We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth ( $$v>0$$ ) and the shrinking ( $$v<0$$ ) regimes of the dynamics. [ABSTRACT FROM AUTHOR]

We study the impact of a hard selective sweep on the genealogy of partially linked neutral loci in the vicinity of the positively selected allele. We consider a sexual population of stochastically varying size and, focusing on two neighboring loci, derive an approximate formula for the neutral genealogy of a sample of individuals taken at the end of the sweep. Individuals are characterized by ecological parameters depending on their genetic type, and governing their growth rate and interactions with other individuals (competition). As a consequence, the `fitness' of an individual depends on the population state and is not an intrinsic characteristic of individuals. We provide a deep insight into the dynamics of the mutant and wild-type populations during the different stages of a selective sweep. [ABSTRACT FROM PUBLISHER]

An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on Γ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved. [ABSTRACT FROM AUTHOR]

We consider a state-dependent $$M_{n}$$ / $$G_{n}$$ /1 queueing system with both finite and infinite buffer sizes. We allow the arrival rate of customers to depend on the number of people in the system. Service times are also state dependent and service rates can be modified at both arrivals and departures of customers. We show that the steady-state solution of this system at arbitrary times can be derived using the supplementary variable method, and that the system's state at arrival epochs can be analyzed using an embedded Markov chain. For the system with infinite buffer size, we first obtain an expression for the steady-state distribution of the number of customers in the system at both arbitrary and arrival times. Then, we derive the average service time of a customer observed at both arbitrary times and arrival epochs. We show that our state-dependent queueing system is equivalent to a Markovian birth-and-death process. This equivalency demonstrates our main insight that the $$M_{n}$$ / $$G_{n}$$ /1 system can be decomposed at any given state as a Markovian queue. Thus, many of the existing results for systems modeled as an M / M / 1 queue can be carried through to the much more practical M / G / 1 model with state-dependent arrival and service rates. Then, we extend the results to the $$M_{n}$$ / $$G_{n}$$ /1 queueing systems with finite buffer size. [ABSTRACT FROM AUTHOR]

An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Г of all locally finite subsets of Rd. The system's states are probability measures on Г the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved. [ABSTRACT FROM AUTHOR]

The connection between a disease and some genetic disorders can be studied by looking for recurrent alterations in genomic profiles of humans affected by the disease. Modeling each patient profile as a 2-state jump Markov process, we define a recurrent alteration in terms of a sojourn time of a cumulated process. The cumulated process happen to be a birth-and-death process. We provide the exact Laplace transforms of relevant hitting times associated with the latter. Based on this exact results, we derive an upper bound of a sojourn time probability of interest. Our upper bound is exactly equal to the p-value nominated in all earlier literature where an attempt is made for an assessment of the significance of genomic alterations. Moreover, that p-value has never been evaluated exactly in previous works. Finally, we give abaques which are useful for the assessment of recurrent genomic alterations for a variety of realistic alteration frequencies and lengths. [ABSTRACT FROM AUTHOR]

Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V. [ABSTRACT FROM AUTHOR]

In this paper, we study an infinite system of point entities in ℝd which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is described by means of a BBGKY-type equation for the corresponding correlation (moment) functions. It is proved that: (a) these functions evolve on a bounded time interval and remain sub-Poissonian due to the competition; (b) in the Vlasov scaling limit they converge to the correlation functions of the time-dependent Poisson point field the density of which solves the kinetic equation obtained in the scaling limit from the equation for the correlation functions. A number of properties of the solutions of the kinetic equation are also esta- blished. [ABSTRACT FROM AUTHOR]

In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of both constant vertex degree graphs and star graphs. The model is motivated by modelling interactions between populations, adsorption-desorption processes and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction. [ABSTRACT FROM AUTHOR]

We study the long-time behaviour of a Markov process evolving in N and conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a unique quasistationary distribution (in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in lawto a unique distribution ρ supported in N* if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes. [ABSTRACT FROM AUTHOR]

We study the probability of extinction for single-type and multi-type continuous-time linear birth-and-death processes in a finite Markovian environment. The probability of extinction is equal to 1 almost surely if and only if the basic reproduction number $$R_0$$ is $$\le 1$$ , the key point being to identify a suitable definition of $$R_0$$ for such a result to hold. [ABSTRACT FROM AUTHOR]

We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide a generic method to construct a Lyapunov function when the drift is a smooth function on RN. This approach gives an elementary and direct proof of ergodicity. We also provide instability conditions. Our main contribution consists of showing how discontinuous drifts change the nature of the stability conditions and of providing generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piecewise constant drifts in dimension two. [ABSTRACT FROM AUTHOR]

Balancing supply and demand for a dockless bike-sharing system is difficult as users are allowed to pick up and return bikes anywhere within a large service area. One strategy to help manage the amount of dockless bikes scattered within a service area is to offer monetary rewards for users who would be willing to pick up bikes scattered around some central location or to return their bikes at this central location. We develop a modeling framework to analyze the effectiveness of using dynamic incentive schemes for balancing the amount of bikes in the system to minimize the expected operating cost. Using an extensive set of numerical experiments, we illustrate specific operation environments under which these dynamic incentive schemes would be most effective for reducing the operating cost of the system. We find that the use of dynamic pickup and return rewards can generate very substantial cost reductions in an operating environment with a high traffic intensity of bike return outside the central location and a high overall traffic intensity of bike returns relative to bike pickups in the system. We also find that return rewards are generally more cost-effective than pickup rewards. • The first to study dynamic incentive schemes in inventory balancing of bike-sharing. • Provide insights in studying effective incentive schemes for bike-sharing firms. • Illustrate specific environments under which these schemes would be most effective. • The pickup/return rewards achieve substantial cost reduction in bike sharing system. • The return rewards are generally more cost-effective than pickup rewards. [ABSTRACT FROM AUTHOR]

Abstract: A competitive stochastic growth model is developed for the simulation of the 3D morphology of eutectic silicon in Al–Si alloys, which represents the colonies of pairwise disconnected Si corals in an Al matrix. The model is based on ideas from stochastic geometry and multivariate time series analysis. The 3D model is validated by comparing morphological characteristics computed for experimental 3D FIB-SEM data, and for realizations drawn from the model. Good agreement between the simulation model and the experimental image data is shown confirming the efficiency of using the competitive stochastic growth model for the generation of virtual eutectic silicon morphologies. [Copyright &y& Elsevier]

We consider a birth-death process {X(t), t ≥ 0} on the positive integers for which the origin is an absorbing state with birth coefficients λn, n > 0, and death coefficients μn, n ≥ 0. If we define ... and ..., where {πn, n ≥ 1} are the potential coefficients, it is a well-known fact (See van Doom (1991)) that if A = ∞ and S < ∞, then λC > 0 and there is precisely one quasistationary distribution, namely, {aj(λC)}, where λC is the decay parameter of {X(t), t ≥ 0) in C = {l, 2, ...} and aj(x) ≡ μ1-1xπjxQj(x), j = 1, 2, .... In this paper we prove that there is a unique quasistationary distribution that attracts all initial distributions supported in C, if and only if the birth-death process {X(t), t ≥ 0} satisfies both A = ∞ and S < ∞. That is, for any probability measure M = {mi, i = 1,2, ...}, we have limt→∞ ℙM(X(t) = j ∣ T > t) = aj(λC), j = 1, 2, ..., where T = inf{t ≥ 0: X(t) = 0} is the extinction time of {X(t), t ≥ 0} if and only if the birth-death process {X(t), t ≥ 0} satisfies both A = ∞ and S < ∞. [ABSTRACT FROM AUTHOR]

General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We also present sufficient conditions that allow us to consider these equations on suitable Banach spaces. [Copyright &y& Elsevier]

Abstract: We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rostʼs totally asymmetric particle model (in discrete time), Simonʼs urban growth model, and Moranʼs infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures. [Copyright &y& Elsevier]

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its master equation, which is a system of linear ODEs with large state space size (N). We derive a single non-linear ODE (called mean-field approximation) for the expected value that yields a good approximation as N tends to infinity. Using only elementary semigroup theory we can prove the order 풪(1/N) convergence of the solution of the system to that of the mean-field equation. The proof holds also for cases that are somewhat more general than the usual density dependent one. Moreover, for Markov chains where the transition rates satisfy some sign conditions, a new approach using a countable system of ODEs for proving convergence to the mean-field limit is proposed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a stochastic model for molecular communication, which accounts for particle dynamics and noise. Differently from existing approaches, we consider that molecules carrying information may interact with the transmission medium. These interactions are modelled by means of absorption, duplication and spontaneous emission phenomena. Using tools from stochastic processes we provide a complete statistical characterization of the evolution over time of the number of molecules present in the transmission medium. The model is applied to the study of flow-based and diffusion-based molecular communication. [Copyright &y& Elsevier]

Abstract: This article deals with quasi- and pseudo-likelihood estimation for a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. [Copyright &y& Elsevier]

We consider the fluid model of a controlled birth-and-death process with an absorbing state. Instead of analyzing the trajectories, we investigate the performance functionals of the underlying process by considering algebraic equations of the dynamic programming type. We provide the accuracy of such fluid approximations and give illustrative examples. [ABSTRACT FROM AUTHOR]

We study a continuous-time stochastic process on strings made of two types of particle, whose dynamics mimic the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global) hydrolysis processes. We give a complete characterization of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process. [ABSTRACT FROM AUTHOR]

Fluid models are used to study functionals of the underlying random processes. Instead of analysing the trajectories, we investigate algebraic equations of the dynamic programming type which turn out to be discrete analogs of the corresponding differential equations. This analysis makes it possible to estimate the accuracy of approximation. Since the algebraic equations are the same for random walks and continuous time birth-and-death processes, we study the two cases in parallel. Several illustrative examples are also presented. [ABSTRACT FROM AUTHOR]

A multi-skill staffing problem in a call center where the agent skill sets are exogenous and the call routing policy has well-specified features of overflow between different agent types is addressed. Constraints are imposed on the service level for each call class, defined here as the steady-state fraction of calls served within a given time threshold, excluded. An approximation of these service levels is developed that allows an arbitrary overflow mechanism and customer abandonment. A two-stage heuristic that finds good solutions to mathematical programs with such constraints is developed. The first stage uses search methods supported by the approximation. Because service level approximation errors may be substantial, the solution is adjusted in a second stage in which performance is estimated by simulation. Realistic problems of varying size and routing policy are solved. The proposed approach is shown to be competitive with (and often better than) previously available methods. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix] [ABSTRACT FROM AUTHOR]