Optimal service rates in the multiserver loss system with heterogeneous servers

1981 ◽  
Vol 18 (03) ◽  
pp. 776-781 ◽  
Author(s):  
G. B. Nath ◽  
E. G. Enns
Keyword(s):  
Heterogeneous System ◽  
Percentage Reduction ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Optimal Service ◽  
Service Rates

A multichannel loss system with heterogeneous servers operating in parallel is analyzed. The sum of the service rates of all servers is assumed constant. The optimal service rates that minimize the probability of losing a customer are obtained, and are shown to be different from each other. The percentage reduction in the probability of losing a customer in the homogeneous and the best heterogeneous system for a few representative values are included.

Optimal service rates in the multiserver loss system with heterogeneous servers

1981 ◽  
Vol 18 (3) ◽  
pp. 776-781 ◽  
Author(s):  
G. B. Nath ◽  
E. G. Enns
Keyword(s):  
Heterogeneous System ◽  
Percentage Reduction ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Optimal Service ◽  
Service Rates

A multichannel loss system with heterogeneous servers operating in parallel is analyzed. The sum of the service rates of all servers is assumed constant. The optimal service rates that minimize the probability of losing a customer are obtained, and are shown to be different from each other. The percentage reduction in the probability of losing a customer in the homogeneous and the best heterogeneous system for a few representative values are included.

Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

1986 ◽  
Vol 23 (01) ◽  
pp. 236-242 ◽  
Author(s):  
Behnam Pourbabai ◽  
David Sonderman
Keyword(s):  
Simulation Study ◽  
Approximation Method ◽  
Counting Process ◽  
Numerical Results ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Utilization Factor ◽  
Service Rates ◽  
Loss Systems ◽  
Server Utilization

Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.

Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

1986 ◽  
Vol 23 (1) ◽  
pp. 236-242 ◽  
Author(s):  
Behnam Pourbabai ◽  
David Sonderman
Keyword(s):  
Simulation Study ◽  
Approximation Method ◽  
Counting Process ◽  
Numerical Results ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Utilization Factor ◽  
Service Rates ◽  
Loss Systems ◽  
Server Utilization

Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.

scholarly journals Robust scheduling for flexible processing networks

2017 ◽  
Vol 49 (2) ◽  
pp. 603-628 ◽  
Author(s):  
Ramtin Pedarsani ◽  
Jean Walrand ◽  
Yuan Zhong
Keyword(s):  
Queueing Networks ◽  
Complex Structure ◽  
Job Flows ◽  
Heterogeneous Servers ◽  
Robust Scheduling ◽  
System Parameters ◽  
Balanced Allocation ◽  
Service Rates ◽  
Length Changes ◽  
Processing Networks

Abstract Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e. policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under nonrestrictive assumptions.

OPTIMAL CONTROL POLICIES FOR AN M/M/1 QUEUE WITH A REMOVABLE SERVER AND DYNAMIC SERVICE RATES

2019 ◽  
pp. 1-21
Author(s):  
Pamela Badian-Pessot ◽  
Mark E. Lewis ◽  
Douglas G. Down
Keyword(s):  
Optimal Control ◽  
Rate Control ◽  
Optimal Policy ◽  
Numerical Experiments ◽  
Service Rate ◽  
Warm Up ◽  
Cost Criterion ◽  
Optimal Service ◽  
Removable Server ◽  
Service Rates

AbstractWe consider an M/M/1 queue with a removable server that dynamically chooses its service rate from a set of finitely many rates. If the server is off, the system must warm up for a random, exponentially distributed amount of time, before it can begin processing jobs. We show under the average cost criterion, that work conserving policies are optimal. We then demonstrate the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number in system. Finally, we present some numerical experiments to provide insights into the practicality of having both a removable server and service rate control.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

A note on a D/G/K loss system with retrials

1990 ◽  
Vol 27 (2) ◽  
pp. 385-392 ◽  
Author(s):  
Behnam Pourbabai
Keyword(s):  
Steady State ◽  
Processing Time ◽  
Distributed Processing ◽  
Random Access ◽  
Heterogeneous Servers ◽  
Loss System ◽  
System A ◽  
Loss Systems

An algorithm is suggested for approximating the performance of a D/G/K loss system with deterministic input, generally distributed processing time, K heterogeneous servers, the random access processing discipline, and retrials in steady state. In loss systems with retrials, the units which at the instants of their arrival at the system find all the servers busy, are not lost: those units retry to be processed by merging with the incoming arrival units. In this system, a fraction of the units which have not initially been processed will be allowed to leave the system. The performance of this system in steady state is approximated by a recursive technique.

ANALYSIS OF MULTI-RESOURCE LOSS SYSTEM WITH STATE-DEPENDENT ARRIVAL AND SERVICE RATES

2017 ◽  
Vol 31 (4) ◽  
pp. 413-419 ◽  
Author(s):  
Valeriy Naumov ◽  
Konstantin Samouylov
Keyword(s):  
Resource Loss ◽  
Loss System ◽  
Negative Customers ◽  
Loss Model ◽  
State Dependent ◽  
Service Rates ◽  
Erlang Loss

In this paper, we study a generalization of the classical multi-dimensional Erlang loss model with state-dependent arrival and service rates, in which customers at arrival occupy random quantities of various resources and release them at departure. Total amount of resources allocated to customers cannot exceed predefined maximum levels. There can be two types of customers: positive customers, which occupy positive quantities of resources, and negative customers, which occupy negative quantities of resources. Negative customers increase the amount of resources available to positive customers and therefore decrease blocking of positive customers caused by lack of resources.

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