This paper describes the Queueing Network Analyzer (QNA), a software package developed at Bell Laboratories to calculate approximate congestion measures for network of queues. The first version QNA analyzes open networks multiserver nodes with first-come, first-served discipline and no capacity constraints. An important feature is that external arrival processes need not be Poisson service-time distributions exponential. Treating other kinds variability important. For example,...

Studies stochastic models of queueing, reliability, inventory, and sequencing in which random influences are considered. One mode--rl is approximated by another that simpler structure or about assumptions can be made. After general results on comparison properties variables processes given, the illustrated application to various queueing questions experimental design, renewal reliability theory, PERT networks branching processes.

This paper analyzes a model of multiplexer for packetized voice and data. A major part the analysis is devoted to characterizing aggregate packet arrival process resulting from superposition separate streams. done via index dispersion intervals (IDI), which describes cumulative covariance among successive interarrival times. The IDI seems very promising as measurement tool characterize complex processes. also delays experienced by data packets in using relatively simple two-parameter approximations.

Two different kinds of heavy-traffic limit theorems have been proved for s-server queues. The first kind involves a sequence queueing systems having fixed number servers with an associated traffic intensities that converges to the critical value one from below. second kind, which is often not thought as heavy traffic, in sequences arrival rates and numbers go infinity while service time distributions remain fixed, being less than one. In each case random variables depicting steady-state...

We present a simple algorithm for numerically inverting Laplace transforms. The is designed especially probability cumulative distribution functions, but it applies to other functions as well. Since does not seem possible provide effective methods with general error bounds, we simultaneously use two different confirm the accuracy. Both are variants of Fourier-series method. first, building on Dubner and Abate (Dubner, H., J. Abate. 1968. Numerical inversion transforms by relating them finite...

This paper initiates an investigation of simple approximations for stochastic point processes. The goal is to develop methods approximately describing complex models such as networks queues and multiechelon inventory systems. proposed approach decouple or decompose the model by replacing all component flows (point processes) independent renewal Here attention focused on ways approximate a single process process. done in two steps: First, properties are used specify few moments interval...

We introduce and investigate a framework for constructing algorithms to invert Laplace transforms numerically. Given transform \hat{f} of complex-valued function nonnegative real-variable, f, the f is approximated by finite linear combination values; i.e., we use inversion formula f(t) \approx f_n (t) \equiv \frac{1}{t} \sum_{k = 0}^{n}\omega_{k}\hat{f}\biggl(\frac{\alpha_{k}}{t}\biggr),\quad 0 < t \infty, where weights ω k nodes α are complex numbers, which depend on n, but do not or...

The queueing systems considered in this paper consist of r independent arrival channels and s service channels, where as usual the are independent. Arriving customers form a single queue served order their without defections. We shall treat two distinct modes operation for channels. In standard system waiting customer is assigned to first available channel servers (servers ≡ channels) shut off when they idle. Thus classical GI / G special case our system. modified that can complete his not...

Many useful descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence for probability measures on function spaces). These typically come standard via the continuous mapping theorem. This paper facilitates applications theorem by determining when several important functions and sequences preserve convergence. The considered are composition, addition, composition plus multiplication, supremum, reflecting barrier, first passage...

Queueing models can usefully represent production systems experiencing congestion due to irregular flows, but exact analyses of these queueing be difficult. Thus it is natural seek relatively simple approximations that are suitably accurate for engineering purposes. Here a basic model developed and evaluated. The the GI/G/m queue, which has m identical servers in parallel, unlimited waiting room, first‐come first‐served queue discipline, with service interarrival times coming from...

This paper is a sequel to [7], in which heavy traffic limit theorems were proved for various stochastic processes arising single queueing facility with r arrival channels and s service channels. Here we prove similar sequences of such facilities. The same behavior prevails many cases this more general setting, but new observed when the sequence intensities associated facilities approaches critical value (ρ = 1) at appropriate rates.

This paper analyzes a mathematical model of blocking system with simultaneous resource possession. There are several multiserver service facilities without extra waiting space at which classes customers arrive in independent Poisson processes. Each customer requests from one server each facility subset the facilities, depending on class. If can be provided immediately upon arrival all required then begins and servers assigned to start finish together. Otherwise, attempt is blocked (lost...

We consider the standard single-server queue with unlimited waiting space and first-in first-out service discipline, but without any explicit independence conditions on interarrival times. find for steady-state waiting-time distribution to have asymptotics of form x –1 log P ( W > ) → – θ ∗as ∞for ∗ 0. require only stationarity basic sequence times minus a Gärtner–Ellis condition cumulant generating function associated partial sums, i.e. n E exp θS ψ as ∞, plus regularity decay rate . The...

We review queueing‐theory methods for setting staffing requirements in service systems where customer demand varies a predictable pattern over the day. Analyzing these is not straightforward, because standard queueing theory focuses on long‐run steady‐state behavior of stationary models. show how to adapt models use nonstationary environments so that time‐dependent performance captured and can be set. Relatively little modification straightforward analysis applies times are short targeted...

Deterministic fluid models are developed to provide simple first-order performance descriptions for multiserver queues with abandonment under heavy loads. Motivated by telephone call centers, the focus is on a large number of servers and nonexponential service-time time-to-abandon distributions. The first model serves as an approximation G/GI/s+GI queueing model, which has general stationary arrival process rate λ, independent identically distributed (IID) service times distribution, s IID...

Call centers usually handle several types of calls, but it is not possible or cost effective to have every agent be able type call. Thus, the agents tend different skills, in combinations. In such an environment, challenging route calls effectively and determine staff requirements. This paper addresses both these routing staffing problems by exploiting limited cross-training. Consistent with literature on flexible manufacturing, we find that minimal flexibility can provide great benefits:...

We establish some general structural results and derive simple formulas describing the time-dependent performance of M t /G/∞ queue (with a nonhomogeneous Poisson arrival process). know that, for appropriate initial conditions, number busy servers at time has distribution each t. Our show how mean function m depends on arrival-rate λ service-time distribution. For example, when is quadratic, m(t) coincides with pointwise stationary approximation λ(t)E[S], where S service time, except lag...

Bivariate distributions with minimum and maximum correlations for given marginal are characterized. Such extremal were first introduced by Hoeffding (1940) Frechet (1951). Several proofs outlined including ones based on rearrangement theorems. The effect of convolution correlation is also studied. Convolution makes arbitrary less extreme while identical measures $R^2$ more extreme. Extreme have applications in data analysis variance reduction Monte Carlo studies, especially the technique...

Although ATM seems to be the wave of future, one analysis requires that utilization network quite low. That is based on asymptotic decay rates steady-state distributions used develop a concept effective bandwidths for connection admission control. The present authors have developed an exact numerical algorithm shows effective-bandwidth approximation can overestimate target small blocking probabilities by several orders magnitude when there are many sources more bursty than Poisson. bad news...