Parijat Dube

Differential join prices for parallel queues: social optimality, dynamic pricing algorithms and application to Internet pricing

We consider a system of identical parallel queues served by a single server and distinguished only by the price charged at entry. A Poisson stream of customers joins the queue by a greedy policy that minimizes a disutility that combines price and congestion. A special case of linear disutility is analyzed for which it is shown that the individually optimal greedy queue join policy is nearly socially optimal. For this queueing system, a Markov decision theoretic framework is formulated for dynamic pricing in the general case. This queueing system has application in the pricing of Internet services.

Queueing analysis of early message discard policy

We consider in this paper packets which arrive according to a Poisson process into a finite queue. A group of consecutive packets forms a frame (or a message) and one then considers not only the quality of service (QoS) of a single packet but also that of the whole message. In order to improve the required QoS, either on the frame loss probabilities or on the delay, discarding mechanisms have to be used. We analyze in this paper the performance of the early message discard (EMD) policy at the buffer, which consists of (1) rejecting an entire message if upon the arrival of the first packet of the message, the buffer occupancy exceeds a threshold K, and (2) if a packet is lost, then all subsequent arrivals that belong to the same message are discarded.

Utility Analysis of Simple FEC Schemes for VoIP

Forward Error Correction (FEC) is an attractive solution for recovering from packet losses in real-time applications. However, in many such applications, due to delay constraints, complex FEC schemes that may enable to approach the Shannon channel capacity cannot be used. In those cases, much simpler FEC schemes are implemented, in which a compressed copy of a packet is concatenated to some subsequent packet. In this paper we analyze the utility gained by such schemes in the case where losses are due to queueing congestion in the network. Loss probabilities in presence of FEC are obtained using sophisticated tools based on Ballot theorems. Our explicit expressions allows us to study numerically several approaches for adding FEC.

TCP over a multi-state Markovian path

In this paper we analyze the performance of a TCP-like flow control mechanism. The transmission rate is considered to increase linearly in time until the receipt of a congestion notification (via loss detection in context of TCP) where the transmission rate is multiplicatively decreased. We introduce a general model based on a multi-state Markov chain for the moments at which the congestion is detected. With this model, we are able to account for correlation and burstiness in congestion moments. Furthermore, we specify several simple versions of our general model and then we identify their parameters from real TCP traces.

Fluid analysis of early message discarding policy under heavy traffic

A message (or a frame) is a group of consecutive packets (or cells in ATM terminology). Often a loss of one packet from the message can result in the loss of the whole message. Selective message discarding policies have been proposed to achieve the twin goal of increased goodput and reduced network congestion by discarding the packets which do not belong to (or have potential of not belonging to) good messages. In this paper we provide a fluid analysis of early message discard. We obtain approximations for performance metrics which are valid for heavy traffic conditions. In particular, we obtain exact expressions for the distribution of the stationary workload process and the fluid goodput ratio. Our analytical results will be quite helpful in selecting an optimal discarding threshold, in studying the sensitivity of goodput ratio to different parameters and also in problems related to buffer and/or capacity dimensioning to achieve a desired quality of service.

On the workload process in a fluid queue with bursty input and selective discarding

In this paper we analyse a finite buffer fluid queue with an on-off Markov Modulated Fluid Process (MMFP) as the arrival process. We call each on-period of the arrival process a message/burst. The queue incorporates a threshold message discarding policy. We work within the framework of Poisson Counter Driven Stochastic Differential equations and obtain the moment generating function and hence the probability density function of the stationary workload process. We then comment on the stability of this fluid queue.

On Loss Probabilities in Presence of Redundant Packets with Random Drop

We study the loss probabilities of messages in an M/M/1/K queueing system where in addition to losses due to buffer overflow there are random losses on the incoming and outgoing links. We focus on the influence of adding redundant packets to the messages. We obtain analytical results that allow us to investigate when does adding redundancy decrease the loss probabilities.

Measurement based optimal source shaping with a shaping + multiplexing delay constraint

Most on-line (i.e., not stored) variable bit rate sources would find it difficult to a priori declare the traffic parameters required by a connection admission control strategy. There is thus the problem of measurement-based on-line estimation of source parameters. In this paper we address the problem of selection of source parameters based on minimising a buffer-bandwidth cost function in the network, for a specified delay QoS violation probability. We consider the shaping delay plus first-hop multiplexing delay; this is adequate, for example, for n statistically identical packet voice sources being multiplexed at a PBX, or in approaches where the end-to-end delay bound is broken into per-hop delay bounds. Our approach yields a leaky bucket rate parameter /spl rho//sup */, and the sum of the shaper buffer and leaky bucket depth (B/sub s/+/spl sigma/). We show that, for a fluid source model, for a linear buffer-bandwidth cost function, and for lossless multiplexing, a sustainable rate parameter of /spl rho//sup */ and burst parameter of 0 yields the minimum cost. We propose and study a stochastic approximation algorithm for on-line estimation of /spl rho//sup */. We then use buffer-bandwidth cost considerations to arrive at an optimal leaky bucket depth /spl sigma//sup */>0 for lossy multiplexing of several statistically identical sources. The computation of /spl sigma//sup */ must be done at the network node. We show, by an example, the improvement in cost that is possible by lossy multiplexing and a positive /spl sigma//sup */.