Optimal Routing to Parallel Servers in Heavy Traffic

2021 ◽  
Author(s):  
Heng-Qing Ye
Keyword(s):  
Heavy Traffic ◽  
Optimal Routing ◽  
Parallel Servers

CHARACTERISTICS OF DETERMINISTIC OPTIMAL ROUTING FOR TWO HETEROGENEOUS PARALLEL SERVERS

2001 ◽  
Vol 12 (06) ◽  
pp. 775-790 ◽  
Author(s):  
K. OIDA ◽  
K. SHINJO
Keyword(s):  
Optimization Problem ◽  
Numerical Solutions ◽  
Heavy Traffic ◽  
Packet Delay ◽  
Optimal Routing ◽  
Service Rate ◽  
Arrival Times ◽  
Average Packet Delay ◽  
Parallel Servers

This paper presents characteristics of optimal routing that assigns each arriving packet to one of two heterogeneous parallel servers, each with its own queue. The characteristics are derived from numerical solutions to an optimization problem, which is to find optimal routing that minimizes the average packet delay under the condition that all of the packets' arrival times as well as all of the packets' sizes are completely known in advance. There are four characteristics: (1) Under light or moderate traffic, the average packet delay of optimal routing is almost the same as that of join the shortest delay (JSD) policy. (2) Under heavier traffic, optimal routing comes to more often use fix queue based on size (FS) policy. (3) Under heavy traffic, optimal routing assigns small packets to the slower server. (4) As the ratio of the slower server's service rate to the faster server's service rate decreases, optimal routing comes to more often use FS policy under light or moderated traffic. These characteristics are verified by the fact that a mimic optimal routing designed based on the four characteristics attains almost the same performance as optimal routing.

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.

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