scholarly journals Optimal Multiserver Scheduling with Unknown Job Sizes in Heavy Traffic

2021 ◽  
Vol 48 (3) ◽  
pp. 136-137
Author(s):  
Ziv Scully ◽  
Isaac Grosof ◽  
Mor Harchol-Balter
Keyword(s):  
Response Time ◽  
Optimal Policy ◽  
Heavy Traffic ◽  
Single Server ◽  
Mean Response Time ◽  
Scheduling Policy

We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In the singleserver k = 1 case, the optimal policy is the Gittins policy, but it is not known whether Gittins or any other policy is optimal in the multiserver case. Exactly analyzing the M/G/k under any scheduling policy is intractable, and Gittins is a particularly complicated policy that is hard to analyze even in the single-server case.

On the optimality and the asymptotic optimality of the smallest weighted available buffer policy

1999 ◽  
Vol 31 (04) ◽  
pp. 1118-1150
Author(s):  
Duan-Shin Lee
Keyword(s):  
Asynchronous Transfer Mode ◽  
Heavy Traffic ◽  
Asymptotic Optimality ◽  
Cell Loss ◽  
Diffusion Limit ◽  
Service Discipline ◽  
Single Server ◽  
Finite Buffers ◽  
Scheduling Policy ◽  
Transfer Mode

A major design challenge of Asynchronous Transfer Mode (ATM) networks is to efficiently provide the quality of service (QOS) specified by users with different demands. We classify sources so that sources in one class join the same buffer and have the same requirement for the ATM cell loss ratio. It is important to search for the service discipline that minimizes the accumulated cell loss under the constraint that the cell loss ratios of the sources are proportional to their QOS requirements. In this paper we consider a model that has N finite buffers and a single server. Buffer i, of size B i , is assigned a positive number w i . The server serves from one of the non-empty buffers whose indices are equal to argmin w i (B i -Q i ), where Q i is the queue length of buffer i. This scheduling policy is called the smallest weighted available buffer policy (SWAB). We show that in a completely symmetric setting, the SWAB policy minimizes the discounted expected loss of cells under some technical conditions. For asymmetric models, we show that the accumulated loss of cells of the SWAB service discipline is asymptotically optimal under heavy traffic conditions in the diffusion limit. Finally, we obtain the expression of w i so that the cell loss ratios of the sources in the diffusion limit are proportional to their QOS requirements.

On the optimality and the asymptotic optimality of the smallest weighted available buffer policy

1999 ◽  
Vol 31 (4) ◽  
pp. 1118-1150
Author(s):  
Duan-Shin Lee
Keyword(s):  
Asynchronous Transfer Mode ◽  
Heavy Traffic ◽  
Asymptotic Optimality ◽  
Cell Loss ◽  
Diffusion Limit ◽  
Service Discipline ◽  
Single Server ◽  
Finite Buffers ◽  
Scheduling Policy ◽  
Transfer Mode

A major design challenge of Asynchronous Transfer Mode (ATM) networks is to efficiently provide the quality of service (QOS) specified by users with different demands. We classify sources so that sources in one class join the same buffer and have the same requirement for the ATM cell loss ratio. It is important to search for the service discipline that minimizes the accumulated cell loss under the constraint that the cell loss ratios of the sources are proportional to their QOS requirements. In this paper we consider a model that has N finite buffers and a single server. Buffer i, of size Bi, is assigned a positive number wi. The server serves from one of the non-empty buffers whose indices are equal to argmin wi(Bi-Qi), where Qi is the queue length of buffer i. This scheduling policy is called the smallest weighted available buffer policy (SWAB). We show that in a completely symmetric setting, the SWAB policy minimizes the discounted expected loss of cells under some technical conditions. For asymmetric models, we show that the accumulated loss of cells of the SWAB service discipline is asymptotically optimal under heavy traffic conditions in the diffusion limit. Finally, we obtain the expression of wi so that the cell loss ratios of the sources in the diffusion limit are proportional to their QOS requirements.

Minimizing Mean Response Time In Batch-Arrival Non-Observable Systems With Single-Server FIFO Queues Operating In Parallel

2021 ◽  
Author(s):  
Mikhail Konovalov ◽  
Rostislav Razumchik
Keyword(s):  
Response Time ◽  
Arrival Time ◽  
Time Instant ◽  
Single Server ◽  
State Information ◽  
Mean Response Time ◽  
Routing Policy ◽  
Long Run ◽  
Service Rates ◽  
Routing Policies

Consideration is given to a dispatching system, where jobs, arriving in batches, cannot be stored and thus must be immediately routed to single-server FIFO queues operating in parallel. The dispatcher can memorize its routing decisions but at any time instant does not have any system's state information. The only information available is the batch/job size and inter-arrival time distributions, and the servers' service rates. Under these conditions, one is interested in the routing policies which minimize the job's long-run mean response time. The single-parameter routing policy is being proposed which, according to the numerical experiments, outperforms best routing rules known by now for non-observable dispatching systems: probabilistic and deterministic. Both the batch-wise and job-wise assignments are studied. Extension to systems with unreliable servers is also addressed.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals Pathwise optimality of the exponential scheduling rule for wireless channels

2004 ◽  
Vol 36 (04) ◽  
pp. 1021-1045 ◽  
Author(s):  
Sanjay Shakkottai ◽  
R. Srikant ◽  
Alexander L. Stolyar
Keyword(s):  
Queue Length ◽  
Wireless Channels ◽  
Unique Feature ◽  
Heavy Traffic ◽  
Wireless Channel ◽  
Service Rate ◽  
Resource Pooling ◽  
Scheduling Policy ◽  
Multiple Data ◽  
Heavy Traffic Limit

We consider the problem of scheduling the transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called the exponential scheduling rule, which was introduced in an earlier paper. Given a system withNusers, and any set of positive numbers {an},n= 1, 2,…,N, we show that in a heavy-traffic limit, under a nonrestrictive ‘complete resource pooling’ condition, this algorithm has the property that, for each timet, it (asymptotically) minimizes maxnanq̃n(t), whereq̃n(t) is the queue length of usernin the heavy-traffic regime.

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