Performance Analysis and Evaluation of Ternary Optical Computer Based on a Queueing System With Synchronous Multi-Vacations

Abstract

The ternary optical computer (TOC) has attracted increasing attention from its providers and potential customers because of the advantages of its optical processor, such as low power consumption, numerous trits, parallelism, dynamical reconfigurability and bitwise allocability. The analysis of its performance has become an urgent problem to be solved in recent years. This paper builds a four-stage TOC service model by introducing synchronous multi-vacations and tandem queueing. Here, a vacation refers specifically to an optical processor vacation. Additionally, we propose a processor-divided-equally(PDE) strategy and a task scheduling and optical processor allocation algorithm under this strategy. Assuming that the intervals of task arrival follow a homogeneous Poisson process, we obtain some important performance indicators, such as the mean response time, mean number of tasks, and optical processor utilization under the PDE strategy, which are based on the M/M/1 and M/M/n queueing systems with exhaustive service and synchronous multivacations. The numerical results illustrate that the number of small optical processors has an important effect on the performance of TOC and that high vacation rate can improve the system performance to some extent. INDEX TERMS Synchronous multi-vacations, tandem queueing, exhaustive service, response time, processor-divided-equally strategy.

Performance analysis and evaluation of ternary optical computer based on asynchronous multiple vacations

“…On the one hand, it submits the operation request to the Server. In Literature [9,19,[34][35][36], Client resolves the operation into binary three-valued logical operations needed to implement the operation when users click on "Submit" button. Meanwhile, it obtains the number of logical operations, the computation amount of each logical operation and the total computation amount and send the operation request to the Server after transforming operands input by user into internal communication codes.…”

“…Literature [9,[34][35][36] all constructed a four-staged TOC service model with vacations. According to the description in Subsection 2.1, this paper has built a three-staged TOC service model with vacations, as shown in Fig.…”

“…The three stages form a tandem queuing model. Compared with Literature [9,[34][35][36], the computing paradigm of TOC proposed in this paper has deleted the preprocessing module in the Server and the service model has only three stages. Therefore, we assert that this model will result in a significant performance improvement over the previous service models.…”

“…In 2017, the TOC platform SD16 with 192 trits was successfully constructed. In 2018, Jin et al built an optical processor(OP) with 1152 trits by combining six SD16s [9]. To solve the carry delay problem, TOC adder [10][11][12][13][14] and multiplier [15,16] were designed and realized based on MSD digital system.…”

“…We focus on making the following contributions in this paper:  This paper first builds a three-staged service model of TOC by connecting three queues --receiving queue, scheduling queue and transmitting queue --in series based on vacation queuing and tandem queuing after illustrating the computing paradigm of a TOC and its primary modules.  Based on the equal partition strategy of OP [9], we propose a TOC task scheduling algorithm with asynchronous vacations of some small OPs(SOPs), a processor allocation algorithm and a processor recovery algorithm.  We construct some analytical al models that evaluates the important performance indicators of TOC, including response time, number of tasks, and OP utilization.…”