A Heavy Traffic Approximation for Queues with Restricted Customer-Server Matchings

We consider a queuing system with n customer classes and m servers. For each class i there is only a subset S(i) of servers that are able to process customer' i requests and they do that using a first-come-first-serve discipline. For this system, we are primarily interested in computing Pij , the steady-state fraction of class-i customers that are served by server j. We also look at stability conditions and standard performance measures like waiting times and queue lengths. Under the assumption that the system is heavy loaded, we approximate Pij as well as the other performance measures. Computational experiments are used to show the quality of our approximations.Operations Management Working Papers Serie

Task Scheduling for Multiprocessor Systems Using Queuing Theory

This research focuses on comparing different multi-processor task scheduling algorithms. Each algorithm has been simulated using one of queuing theory models in Operations Research (OR) science to evaluate its behavior and efficiency. The comparison includes an analysis of the behavior of central processing unit (CPU) when receiving number of jobs at four random job duration patterns that are; (random, ascending, descending, and volatile low-high). Microsoft Excel 2010 was used to form the data of each case, and the result shows convergence and divergence among the studied algorithms at different patterns. Also it has been found that the Fleischer algorithm is very efficient in enhancing and minimizing the waiting duration for each job at the total job queue of the CPU. Keywords: Operations Research, Queuing Theory, Multiprocessor, Scheduling Algorithms, Simulation

A Study of Application-awareness in Software-defined Data Center Networks

A data center (DC) has been a fundamental infrastructure for academia and industry for many years. Applications in DC have diverse requirements on communication. There are huge demands on data center network (DCN) control frameworks (CFs) for coordinating communication traffic. Simultaneously satisfying all demands is difficult and inefficient using existing traditional network devices and protocols. Recently, the agile software-defined Networking (SDN) is introduced to DCN for speeding up the development of the DCNCF. Application-awareness preserves the application semantics including the collective goals of communications. Previous works have illustrated that application-aware DCNCFs can much more efficiently allocate network resources by explicitly considering applications needs. A transfer application task level application-aware software-defined DCNCF (SDDCNCF) for OpenFlow software-defined DCN (SDDCN) for big data exchange is designed. The SDDCNCF achieves application-aware load balancing, short average transfer application task completion time, and high link utilization. The SDDCNCF is immediately deployable on SDDCN which consists of OpenFlow 1.3 switches. The Big Data Research Integration with Cyberinfrastructure for LSU (BIC-LSU) project adopts the SDDCNCF to construct a 40Gb/s high-speed storage area network to efficiently transfer big data for accelerating big data related researches at Louisiana State University. On the basis of the success of BIC-LSU, a coflow level application-aware SD- DCNCF for OpenFlow-based storage area networks, MinCOF, is designed. MinCOF incorporates all desirable features of existing coflow scheduling and routing frame- works and requires minimal changes on hosts. To avoid the architectural limitation of the OpenFlow SDN implementation, a coflow level application-aware SDDCNCF using fast packet processing library, Coflourish, is designed. Coflourish exploits congestion feedback assistances from SDN switches in the DCN to schedule coflows and can smoothly co-exist with arbitrary applications in a shared DCN. Coflourish is implemented using the fast packet processing library on an SDN switch, Open vSwitch with DPDK. Simulation and experiment results indicate that Coflourish effectively shortens average application completion time

Modelling energy efficiency and performance trade-offs

PhD ThesisPower and energy consumption in data centres is a huge concern for data centre providers. As a result, this work considers the modelling and analysis of policy and scheduling schemes using Markovian processing algebra known as PEPA. The first emphasis was on modelling an energy policy in PEPA that dynamically controls the powering servers ON or OFF. The focus is to identify and reflect the trade-off between saving energy (by powering down servers) and performance cost. While powering down servers saves energy, it could increase the performance cost. The research analyses the effect of the policy on energy consumption and performance cost, with different combinations of dynamic and static servers used in the policy against different scenarios, including changes in job arrival rate, job arrival duration and the time needed by servers to be powered On and start process jobs. The result gave interesting outcomes because every scenario is unique, and therefore, no server combinations were found to give low energy and high performance in all situations. The second focus was to consider the impact of scheduler’s choice on performance and energy under unknown service demands. Three algorithms were looked at: task assignment based on guessing size (TAGS), the shortest queue strategy and random allocation. These policies were modelled using PEPA to derive numerical solutions in a two servers system. The performance was analysed considering throughput, average response time and servers’ utilisation. At the same time, the energy consumption was in terms of total energy consumption and energy consumption per job. The intention was to analyse the performance and energy consumption in a homogeneous and heterogeneous environment, and the environment was assumed to be homogeneous in the beginning. However, the service distribution was considered either a negative exponential (hence relatively low variance) or a two-phase hyper-exponential (relatively high variance) in each policy. In all cases, the arrival process has been assumed to be a Poisson stream, and the maximum queue lengths are finite (maximum size is 10 jobs). The performance results showed that TAGS performs worse under exponential - vii - distribution and the best under two-phase hyper-exponential. TAGS produce higher throughput and lower job loss when service demand has an H2 distribution. Our results show that servers running under TAGS consume more energy than other policies regarding total energy consumption and energy per job under exponential distribution. In contrast, TAGS consumes less energy per job than the random allocation when the arrival rate is high, and the job size is variable (two-phase hyper-exponential). In a heterogeneous environment and based on our results on the homogeneous environment, the performance metrics and energy consumption was analysed only under twophase hyper-exponential. TAGS works well in all server configurations and achieves greater throughput than the shortest queue or weighted random, even when the second server’s speed was reduced by 40% of the first server’s in TAGS. TAGS outperforms both the shortest queue and weighted random, whether their second server is faster or slower than the TAGS second server. The system’s heterogeneity did not significantly improve or decrease TAGS throughput results. Whether the second server is faster or slower, even when the arrival rate is less than 75% of the system capacity, it approximately showed no effect. On the other hand, heterogeneity of the system has a notable effect on the throughput of the shortest queue and weighted random. The decrease or increase in throughput follows the trend of the second server performance capability. In terms of total energy consumption, for all scheduling schemes, when the second server is slower than the first server, the energy consumption is the highest among all scenarios for each arrival rate. TAGS was the worst and consumed higher energy than both the shortest queue strategy and weighted random allocation. However, in terms of energy per job, when servers are identical, or server2 is faster, it was observed that the shortest queue is the optimal strategy as long as the incoming jobs rate does not exceed 70% of the system capacity ( arrival rate <15). Furthermore, the TAGS was the best strategy when the incoming task rate exceeds 70% of the system capacity. So, as more jobs are produced, the energy per job decreases eventually. Choosing the energy policy or scheduling algorithm will impact energy consumption and performance either negatively or positively