Pricing strategies under heterogeneous service requirements

This paper analyzes a communication network, used by customers with heterogeneous service requirements. We investigate priority queueing as a way to establish service differentiation. It is assumed that there is an infinite population of customers, who join the network as long as their utility (which is a function of the queueing delay) is larger than the price of the service. We focus on the specific situation with two types of users: one type is delay-sensitive (`voice'), whereas the other is delay-tolerant (`data'); these preferences are reflected in their utility curves. Two models are considered: in the first the network determines the priority class of the users, whereas the second model leaves this choice to the users. For both models we determine the prices that maximize the provider's profit. Importantly, these situations do not coincide. Our analysis uses elements from queueing theory, but also from microeconomics and game theory (e.g., the concept of a Nash equilibrium). We conclude the paper by considering a model in which throughput (rather than delay) is the main performance measure. Again the pricing strategy exploits the heterogeneity in service requirements and willingness-to-pay

Analysis of jitter due to call-level fluctuations

In communication networks used by constant bit rate applications, call-level dynamics (i.e., entering and leaving calls) lead to fluctuations in the load, and therefore also fluctuations in the delay (jitter). By intentionally delaying the packets at the destination, one can transform the perturbed packet stream back into the original periodic stream; in other words: there is a trade off between jitter and delay, in that jitter can be removed at the expense of delay. As a consequence, for streaming applications for which the packet delay should remain below some predefined threshold, it is desirable that the jitter remains small. This paper presents a set of procedures to compute the jitter due to call-level variations. We onsider a network resource shared by a fluctuating set of constant bit rate applications (modelled as periodic sources). As a first step we study the call-level dynamics: supposing that a tagged call sees n0 calls when entering the system, then we compute the probability that at the end of its duration (consisting of, say, i packets) ni calls are present, of which n0,i stem from the original n0 calls. As a second step, we show how to compute the jitter, for given n0, ni, and n0,i; in this analysis generalized Ballot-problems have to be solved. We find an iterative exact solution to these, and explicit approximations and bounds. Then, as a final step, the (packet-level) results of the second step are weighed with the (call-level) probabilities of the first step, thus resulting in the probability distribution of the jitter experienced within the call duration. An explicit Gaussian approximation is proposed. Extensive numerical experiments validate the accuracy of the approximations and bound

Large deviations for complex buffer architectures: the short-range dependent case

This paper considers Gaussian flows multiplexed in a queueing network, where the underlying correlation structure is assumed to be short-range dependent. Whereas previous work mainly focused on the FIFO setting, this paper addresses overflow characteristics of more complex buffer architectures. We subsequently analyze the tandem queue, a priority system, and generalized processor sharing. In a many-sources setting, we explicitly compute the exponential decay rate of the overflow probability. Our study relies on large-deviations arguments, e.g., Schilder's theore

Simulation-based computation of the workload correlation function in a Levy-driven queue

In this paper we consider a single-server queue with Levy input, and in particular its workload process (Q_t), focusing on its correlation structure. With the correlation function defined as r(t) := Cov(Q_0, Q_t)/Var Q_0 (assuming the workload process is in stationarity at time 0), we first study its Laplace transform, both for the case that the Levy process has positive jumps, and that it has negative jumps. These expressions allow us to prove that r(·) is positive, decreasing, and convex, relying on the machinery of completely monotone functions. For the light-tailed case, we estimate the behavior of r(t) for t large. We then focus on techniques to estimate r(t) by simulation. Naive simulation techniques require roughly (r(t))^{−2} runs to obtain an estimate of a given precision, but we develop a coupling technique that leads to substantial variance reduction (required number of runs being roughly (r(t))^{−1}). If this is augmented with importance sampling, it even leads to a logarithmically efficient algorithm

On the record process of time-reversible spectrally-negative Markov additive processes

We study the record process of a spectrally-negative Markov additive process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs with negative drift, or, equivalently, the stationary workload distribution of the associated storage system; the focus is on Markov-modulated Brownian mo- tion, spectrally-negative and spectrally-positive MAPs. It is also argued how our results are of great help in the numerical analysis of systems in which the driving MAP is a superposition of multiple time-reversible MAPs

Sojourn times in the M/G/1 FB queue with light-tailed service times

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the Foreground-Background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimises the decay rate in the class of work-conserving disciplines

Flow-level models for multipath routing

In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation is identified, and we describe a finite algorithm to find this rate allocation and the clustering explicitly. Then we consider the dynamic model, in which there are stochastic arrivals and departures; we do so for models with both streaming and elastic traffic, and where a peak-rate is imposed on the elastic flows (to be thought of as an access rate). Lacking explicit expressions for the equilibrium distribution of the Markov process under consideration, we study its fluid and diffusion limits; in particular, we prove uniqueness of the equilibrium point. We demonstrate through a specific example how the diffusion limit can be identified; it also reveals structural results about the clustering pattern when the minimal rate is very small and the network grows large

On spectral simulation of fractional Brownian motion

This paper focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class of approximate methods that are based on the spectral properties of fBm's stationary incremental process, usually called fractional Gaussian noise (fGn). The main contribution is a proof of asymptotical exactness (in a sense that is made precise) of these spectral methods. Moreover, we establish the connection between the spectral simulation approach and a widely used method, originally proposed by Paxson, that lacked a formal mathematical justification. The insights enable us to evaluate the Paxson method in more detail. It is also shown that spectral simulation is related to the fastest known exact method

Simulation-based computation of the workload correlation function in a Lévy-driven queue

In this paper we consider a single-server queue with Levy input, and in particular its workload process (Q_t), focusing on its correlation structure. With the correlation function defined as r(t) := Cov(Q_0,Q_t)/Var(Q_0) (assuming the workload process is in stationarity at time 0), we first study its transform with respect to t, both for the case that the Levy process has positive jumps, and that it has negative jumps. These expressions allow us to prove that r(·) is positive, decreasing, and convex, relying on the machinery of completely monotone functions. For the light-tailed case, we estimate the behavior of r(t) for t large. We then focus on techniques to estimate r(t) by simulation. Naive simulation techniques require roughly (r(t))^{?2} runs to obtain an estimate of a given precision, but we develop a coupling technique that leads to substantial variance reduction (required number of runs being roughly (r(t))^{?1}). If this is augmented with importance sampling, it even leads to a logarithmically efficient algorithm