OPTIMAL ROUTING IN OUTPUT-QUEUED FLEXIBLE SERVER SYSTEMS

2005 ◽  
Vol 19 (2) ◽  
pp. 141-189 ◽  
Author(s):  
Alexander L. Stolyar
Keyword(s):  
Heavy Traffic ◽  
Asymptotic Optimality ◽  
Optimal Routing ◽  
Asymptotic Regime ◽  
Resource Pooling ◽  
Strictly Convex ◽  
Flexible Servers ◽  
Server Systems ◽  
Optimality Properties ◽  
Flexible Server

We consider a queuing system with multitype customers and nonhomogeneous flexible servers, in the heavy traffic asymptotic regime and under a complete resource pooling (CRP) condition. For the input-queued (IQ) version of such a system (with customers being queued at the system “entrance,” one queue per each type), it was shown in the work of Mandelbaum and Stolyar that a simple parsimonious Gcμ scheduling rule is optimal in that it asymptotically minimizes the system customer workload and some strictly convex queuing costs. In this article, we consider a different—output-queued (OQ)—version of the model, where each arriving customer must be assigned to one of the servers immediately upon arrival. (This constraint can be interpreted as immediate routing of each customer to one of the “output queues,” one queue per each server.) Consequently, the space of controls allowed for an OQ system is a subset of that for the corresponding IQ system.We introduce the MinDrift routing rule for OQ systems (which is as simple and parsimonious as Gcμ) and show that this rule, in conjunction with arbitrary work-conserving disciplines at the servers, has asymptotic optimality properties analogous to those Gcμ rule has for IQ systems. A key element of the analysis is the notion of system server workload, which, in particular, majorizes customer workload. We show that (1) the MinDrift rule asymptotically minimizes server workload process among all OQ-system disciplines and (2) this minimal process matches the minimal possible customer workload process in the corresponding IQ system. As a corollary, MinDrift asymptotically minimizes customer workload among all disciplines in either the OQ or IQ system.

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

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.

DYNAMIC ASSIGNMENT OF DEDICATED AND FLEXIBLE SERVERS IN TANDEM LINES

2007 ◽  
Vol 21 (4) ◽  
pp. 497-538 ◽  
Author(s):  
Sigrún Andradóttir ◽  
Hayriye Ayhan ◽  
Douglas G. Down
Keyword(s):  
Average Throughput ◽  
Buffer Space ◽  
Dynamic Assignment ◽  
Flexible Servers ◽  
Long Run ◽  
Cross Training ◽  
Service Rates ◽  
Dedicated Servers ◽  
Flexible Server

Consider a system of queuing stations in tandem having both flexible servers (who are capable of working at multiple stations) and dedicated servers (who can only work at the station to which they are dedicated). We study the dynamic assignment of servers to stations in such systems with the goal of maximizing the long-run average throughput. We also investigate how the number of flexible servers influences the throughput and compare the improvement that is obtained by cross-training another server (i.e., increasing flexibility) with the improvement obtained by adding a resource (i.e., a new server or a buffer space). Finally, we show that having only one flexible server is sufficient for achieving near-optimal throughput in certain systems with moderate to large buffer sizes (the optimal throughput is attained by having all servers flexible). Our focus is on systems with generalist servers who are equally skilled at all tasks, but we also consider systems with arbitrary service rates.

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