An infinite server system with customer-to-server packing constraints

Author(s):  
Alexander L. Stolyar
2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.


2019 ◽  
Vol 47 (6) ◽  
pp. 513-520
Author(s):  
Mariska Heemskerk ◽  
Michel Mandjes

2013 ◽  
Vol 61 (5) ◽  
pp. 1200-1217 ◽  
Author(s):  
Alexander L. Stolyar

2015 ◽  
Vol 47 (3) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.


Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4089
Author(s):  
Kaiqiang Zhang ◽  
Dongyang Ou ◽  
Congfeng Jiang ◽  
Yeliang Qiu ◽  
Longchuan Yan

In terms of power and energy consumption, DRAMs play a key role in a modern server system as well as processors. Although power-aware scheduling is based on the proportion of energy between DRAM and other components, when running memory-intensive applications, the energy consumption of the whole server system will be significantly affected by the non-energy proportion of DRAM. Furthermore, modern servers usually use NUMA architecture to replace the original SMP architecture to increase its memory bandwidth. It is of great significance to study the energy efficiency of these two different memory architectures. Therefore, in order to explore the power consumption characteristics of servers under memory-intensive workload, this paper evaluates the power consumption and performance of memory-intensive applications in different generations of real rack servers. Through analysis, we find that: (1) Workload intensity and concurrent execution threads affects server power consumption, but a fully utilized memory system may not necessarily bring good energy efficiency indicators. (2) Even if the memory system is not fully utilized, the memory capacity of each processor core has a significant impact on application performance and server power consumption. (3) When running memory-intensive applications, memory utilization is not always a good indicator of server power consumption. (4) The reasonable use of the NUMA architecture will improve the memory energy efficiency significantly. The experimental results show that reasonable use of NUMA architecture can improve memory efficiency by 16% compared with SMP architecture, while unreasonable use of NUMA architecture reduces memory efficiency by 13%. The findings we present in this paper provide useful insights and guidance for system designers and data center operators to help them in energy-efficiency-aware job scheduling and energy conservation.


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