K. R. Jogesh Muppala

Stiffness-tolerant methods for transient analysis of stiff Markov chains

Abstract Three methods for numerical transient analysis of Markov chains, the modified Jensens method (Jensens method with steady-state detection of the underlying DTMC and computation of Poisson probabilities using the method of Fox and Glynn [1]), a third-order L-stable implicit Runge-Kutta method, and a second-order L-stable method, TR-BDF2, are compared. These methods are evaluated on the basis of their performance (accuracy of the solution and computational cost) on stiff Markov chains. Steady-state detection in Jensens method results in large savings of computation time for Markov chains when mission time extends beyond the steady-state point. For stiff models, computation of Poisson probabilities using traditional methods runs into underflow problems. Fox and Glynns method for computing Poisson probabilities avoids underflow problems for all practical problems and yields highly accurate solutions. We conclude that for mildly stiff Markov chains, the modified Jensens method is the method of choice. For stiff Markov chains, we recommend the use of the L-stable ODE methods. If low accuracy (upto eight decimal places) is acceptable, then TR-BDF2 method should be used. If higher accuracy is desired, then we recommend third-order implicit Runge-Kutta method.

FlatNet: Towards a flatter data center network

The design of the data center network that interconnects the massive number of servers is very important to ensure the agility and robustness of the data center to meet the requirements of the applications. In response to this challenge, the research community have begun exploring novel interconnect topologies including FatTree, DCell, BCube, HyPaC, etc. However, the solutions proposed so far either scale too slowly, suffer from performance bottlenecks, are server-location dependent, inherit poor availability, or can be too complex/expensive to construct. Motivated by these very important challenges, we propose a new data center interconnect called FlatNet that combines the advantages of previous architectures while avoiding their limitations. FlatNet is a cost-effective, high-performance, reliable and scalable interconnect with almost flat architecture. For example, given an equal-sized data center, the costs of a FlatNet in terms of number of links and switches are roughly 2/3 and 2/5 that of Portland, while still delivering comparable overall performance.

Numerical computation of response time distributions using stochastic reward nets

We consider the numerical computation of response time distributions for closed product form queueing networks using thetagged customer approach. We map this problem on to the computation of the time to absorption distribution of a finite-state continuous time Markov chain. The construction and solution of these Markov chains is carried out using a variation of stochastic Petri nets called stochastic reward nets (SRNs). We examine the effects of changing the service discipline and the service time distribution at a queueing center on the response time distribution. A multiserver queueing network example is also presented. While the tagged customer approach for computing the response time distribution is not new, this paper presents a new approach for computing the response time distributions using SRNs.

VoIP performance on differentiated services enabled network

We study the performance of voice over Internet protocol (VoIP) traffic aggregates over differentiated services (Diffserv) enabled network using expedited forwarding (EF) per hop behavior (PHB). We compare the delay and jitter performance of the VoIP traffic generated by different standard voice codec algorithms, both under Diffserv with EF PHB and with best-effort service. Both homogenous and heterogenous voice traffic aggregates are considered. Our results show that the use of EF yields very good performance improvement for voice traffic compared to best-effort. The improvement is greatest for high coding rate algorithms like G.711 than lower coding rate algorithms like G.723.1. For heterogenous traffic aggregates, the traffic from higher bit rate codecs obtains a better performance compared to lower bit rate codecs.

Performance evaluation of multiple input-queued ATM switches with PIM scheduling under bursty traffic

In this letter, we analyze the performance of multiple input-queued asynchronous transfer mode (ATM) switches that use parallel iterative matching (PIM) for scheduling the transmission of head-of-line cells in the input queues. A queueing model of the switch is developed under independently, identically distributed, two-state Markov modulated Bernoulli processes bursty traffic. The underlying Markov chain of the queueing model is a quasi-birth-death (QBD) chain. The QBD chain is solved using an iterative computing method. Interesting performance metrics of the ATM switch such as the throughput, the mean cell delay, and the cell loss probability can be derived from the model. Numerical results from both the analytical model and simulation are presented, and the accuracy of the analysis is briefly discussed.

A general framework for performance guaranteed green data center networking

From the perspective of resource allocation and routing, this paper aims to save as much energy as possible in data center networks. We present a general framework, based on the blocking island paradigm, to try to maximize the network power conservation and minimize sacrifices of network performance and reliability. The bandwidth allocation mechanism together with power-aware routing algorithm achieve a bandwidth guaranteed tighter network. Besides, our fast efficient heuristics for allocating bandwidth enable the system to scale to large sized data centers. The evaluation result shows that up to more than 50% power savings are feasible while guaranteeing network performance and reliability.

Defects per Million Computation in Service-Oriented Environments

Traditional system-oriented dependability metrics like reliability and availability do not fully reflect the impact of system failure-repair behavior in service-oriented environments. The telecommunication systems community prefers to use Defects Per Million (DPM), defined as the number of calls dropped out of a million calls due to failures, as a user-perceived dependability metric. In this paper, we provide new formulation for the computation of the DPM metric for a system supporting Voice over IP functionality using the Session Initiation Protocol (SIP). We evaluate different replication schemes that can be used at the SIP application server. They include the effects of software failure, failure detection, recovery mechanisms, and imperfect coverage for recovery mechanisms. We derive closed-form expressions for the DPM taking into account the transient behavior of recovery after a failure. Our approach and underlying models can be readily extended to other types of service-oriented environments.

Analysis of non-blocking ATM switches with multiple input queues

The performance of a non-blocking ATM switch in which each input port maintains a separate queue for each output port to overcome the head-of-line (HOL) blocking of conventional FIFO input queuing switches is presented. Parallel iterative matching (PIM) is used as the scheduling algorithm for selecting the HOL cells to be transmitted in each time slot. After deriving a closed-form solution for the maximum throughput of the switch under saturated conditions, an analytical model for evaluating the switch performance under i.i.d Bernoulli traffic is developed using the tagged input queue approach. Performance measures including throughput, mean cell delay, and cell loss probability are computed from the analytical model. The accuracy of the analytical model is verified using simulation.

Designing Packet Buffers Using Random Round Robin

High-speed routers rely on well-designed packet buffers that support multiple queues, large capacity and short response times. Some researchers suggested combined SRAM/DRAM hierarchical buffer architectures to meet these challenges. However, these architectures suffer from either large SRAM requirement or high time-complexity in the memory management. Our analysis indicates that they perform exactly the same in the worst case. In this paper, we present a novel packet buffer architecture which reduces the SRAM size requirement by (k-1)/2k, where k denotes the number of DRAMs working in parallel. We use a fast batch load scheme and per-queue Random Round Robin memory management algorithm. Our mathematical analysis and simulation results indicate that the proposed architecture provides guaranteed performance in terms of low time complexity, short access delay and upper-bounded drop rate, when a little speedup is provided.

Analytical analysis of ATM switches with multiple input queues with bursty traffic

A queueing model for a novel multiple input-queued ATM switch under i.i.d bursty traffic modeled by 2-state Markov modulated Bernoulli processes (MMBPs) is proposed. A quasi-birth-death (QBD) chain is constructed as the underlying Markov chain of the queueing model. Each input port of the switch maintains N separate queues each for buffering cells destined to one of the N outputs and an efficient randomized parallel algorithm, called parallel iterative matching (PIM) is used by the switch to schedule the head-of-line (HOL) cells of the input queues out to the output queues. The QBD chain is solved by finding the fixed point of the introduced fixed point equation using an iterative computing scheme. Interesting performance parameters of the switch such as the throughput, the mean cell delay and the cell loss probability are derived from the solved QBD chain. Numerical results from both the analytical model and simulations are presented and the accuracy of the analysis is discussed. The queueing model can be extended using the same technique to the situation where complicated bursty traffic with more states is asserted to the switch.