We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existin...We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existing schemes either consider slot-by-slot scheduling with queue depth serving as the delay metric or assume that each input-output connection has the same delay bound in the batch scheduling mode. The former scheme neglects the effect of reconfiguration overhead, which may result in crippled system performance, while the latter cannot satisfy users' differentiated Quality of Service(Qo S) requirements. To make up these deficiencies, we propose a new batch scheduling scheme to meet the various portto-port delay requirements in a best-effort manner. Moreover, a speedup is considered to compensate for both the reconfiguration overhead and the unavoidable slots wastage in the switch fabric. With traffic matrix and delay constraint matrix given, this paper proposes two heuristic algorithms Stringent Delay First(SDF) and m-order SDF(m-SDF) to realize the 100% packet switching, while maximizing the delay constraints satisfaction ratio. The performance of our scheme is verified by extensive numerical simulations.展开更多
In this paper,the existence and growth of entire solutions of some type of nonlinear delay-differential equations are studied.Using Cartan's second main theorem and Nevanlinna theory of meromorphic functions,we ob...In this paper,the existence and growth of entire solutions of some type of nonlinear delay-differential equations are studied.Using Cartan's second main theorem and Nevanlinna theory of meromorphic functions,we obtain the exact forms of its entire solutions with hyperorder less than one.展开更多
This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities...This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.展开更多
In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay diffe...In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation;O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.展开更多
In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples ar...In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.展开更多
The pandemic of novel coronavirus disease 2019(COVID-19)has been a severe threat to public health.The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak....The pandemic of novel coronavirus disease 2019(COVID-19)has been a severe threat to public health.The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak.In this paper,we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine,and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine.The model is established based on the combination of the compartmental model and individual-based model simulations,which results in a closed-form delay differential equation model.The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate.The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient.We applied the model to study the effectiveness of contact tracing and quarantine.The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model,however,it is not enough to describe the diverse response due to the stochastic effect.Based on model simulations,we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size,however,may not be enough to achieve zero-infectious in a short time,a combination of close contact quarantine and social contact restriction is required to achieve zeroinfectious.Moreover,the effect of reducing epidemic size is insensitive to the period of quarantine,there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.展开更多
基金supported by the Major State Basic Research Program of China (973 project No. 2013CB329301 and 2010CB327806)the Natural Science Fund of China (NSFC project No. 61372085, 61032003, 61271165 and 61202379)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China (RFDP project No. 20120185110025, 20120185110030 and 20120032120041)supported by Tianjin Key Laboratory of Cognitive Computing and Application, School of Computer Science and Technology, Tianjin University, Tianjin, P. R. China
文摘We consider differentiated timecritical task scheduling in a N×N input queued optical packet s w itch to ens ure 100% throughput and meet different delay requirements among various modules of data center. Existing schemes either consider slot-by-slot scheduling with queue depth serving as the delay metric or assume that each input-output connection has the same delay bound in the batch scheduling mode. The former scheme neglects the effect of reconfiguration overhead, which may result in crippled system performance, while the latter cannot satisfy users' differentiated Quality of Service(Qo S) requirements. To make up these deficiencies, we propose a new batch scheduling scheme to meet the various portto-port delay requirements in a best-effort manner. Moreover, a speedup is considered to compensate for both the reconfiguration overhead and the unavoidable slots wastage in the switch fabric. With traffic matrix and delay constraint matrix given, this paper proposes two heuristic algorithms Stringent Delay First(SDF) and m-order SDF(m-SDF) to realize the 100% packet switching, while maximizing the delay constraints satisfaction ratio. The performance of our scheme is verified by extensive numerical simulations.
基金Supported by the National Natural Science Foundation of China(Grant No.12261044)the STP of Education Department of Jiangxi Province(Grant No.GJJ210302)。
文摘In this paper,the existence and growth of entire solutions of some type of nonlinear delay-differential equations are studied.Using Cartan's second main theorem and Nevanlinna theory of meromorphic functions,we obtain the exact forms of its entire solutions with hyperorder less than one.
基金partially supported by the NSFC(12061042)the NSF of Jiangxi(20202BAB201003)+3 种基金the support of the National Science Center(Poland)via grant 2017/25/B/ST1/00931partially supported by the Project PID2021-124472NB-I00funded by MCIN/AEI/10.13039/501100011033by"EFDF A way of making Europe"。
文摘This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.
文摘In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation;O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.
基金The first author is supported by NPU Foundation for Fundamental Research （NPU-FFR-JC20100220） the second author is supported by National Natural Science Foundation （Grant No. 11031002） and RFDP the third author is supported by National Natural Science Foundation （Grant No. 11071048 ）
文摘In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.
基金supported by the National Natural Science Foundation of China(No.11831015).
文摘The pandemic of novel coronavirus disease 2019(COVID-19)has been a severe threat to public health.The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak.In this paper,we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine,and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine.The model is established based on the combination of the compartmental model and individual-based model simulations,which results in a closed-form delay differential equation model.The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate.The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient.We applied the model to study the effectiveness of contact tracing and quarantine.The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model,however,it is not enough to describe the diverse response due to the stochastic effect.Based on model simulations,we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size,however,may not be enough to achieve zero-infectious in a short time,a combination of close contact quarantine and social contact restriction is required to achieve zeroinfectious.Moreover,the effect of reducing epidemic size is insensitive to the period of quarantine,there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.
