Extremal properties of the shortest/longest non-full queue policies in finite-capacity systems with state-dependent service rates

1993 ◽  
Vol 30 (1) ◽  
pp. 223-236 ◽  
Author(s):  
P. D. Sparaggis ◽  
D. Towsley ◽  
C. G. Cassandras
Keyword(s):  
Optimal Allocation ◽  
Buffer Allocation ◽  
Performance Indices ◽  
Parallel Queues ◽  
State Dependent ◽  
Weak Majorization ◽  
Service Rates ◽  
Queue Lengths ◽  
Buffer Capacities ◽  
Extremal Properties

We consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. We establish the extremal properties of the shortest non-full queue (SNQ) and the longest non-full queue (LNQ) policies, in systems with concave/convex service rates. Our analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, we solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme', in the sense of capacity balancing. Some extensions are also discussed.

Extremal properties of the shortest/longest non-full queue policies in finite-capacity systems with state-dependent service rates

1993 ◽  
Vol 30 (01) ◽  
pp. 223-236 ◽  
Author(s):  
P. D. Sparaggis ◽  
D. Towsley ◽  
C. G. Cassandras
Keyword(s):  
Optimal Allocation ◽  
Buffer Allocation ◽  
Performance Indices ◽  
Parallel Queues ◽  
State Dependent ◽  
Weak Majorization ◽  
Service Rates ◽  
Queue Lengths ◽  
Buffer Capacities ◽  
Extremal Properties

We consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. We establish the extremal properties of the shortest non-full queue (SNQ) and the longest non-full queue (LNQ) policies, in systems with concave/convex service rates. Our analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, we solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme', in the sense of capacity balancing. Some extensions are also discussed.

Braess's paradox in a queueing network with state-dependent routing

1997 ◽  
Vol 34 (01) ◽  
pp. 134-154 ◽  
Author(s):  
Bruce Calvert ◽  
Wiremu Solomon ◽  
Ilze Ziedins
Keyword(s):  
Queueing Network ◽  
Wheatstone Bridge ◽  
The Other ◽  
Time Of Arrival ◽  
Expected Time ◽  
Initial Network ◽  
Braess’S Paradox ◽  
State Dependent ◽  
Service Rates ◽  
Queue Lengths

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential. We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them. We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Braess's paradox in a queueing network with state-dependent routing

1997 ◽  
Vol 34 (1) ◽  
pp. 134-154 ◽  
Author(s):  
Bruce Calvert ◽  
Wiremu Solomon ◽  
Ilze Ziedins
Keyword(s):  
Queueing Network ◽  
Wheatstone Bridge ◽  
The Other ◽  
Time Of Arrival ◽  
Expected Time ◽  
Initial Network ◽  
Braess’S Paradox ◽  
State Dependent ◽  
Service Rates ◽  
Queue Lengths

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential.We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them.We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Optimal Control of State-Dependent Service Rates in a MAP/M/1 Queue

2017 ◽  
Vol 62 (10) ◽  
pp. 4965-4979 ◽  
Author(s):  
Li Xia ◽  
Qi-Ming He ◽  
Attahiru Sule Alfa
Keyword(s):  
Optimal Control ◽  
State Dependent ◽  
Service Rates

scholarly journals Using Computer Simulation Method to Improve Throughput of Production Systems by Buffers and Workers Allocation

2015 ◽  
Vol 6 (4) ◽  
pp. 60-69 ◽  
Author(s):  
Sławomir Kłos ◽  
Peter Trebuna
Keyword(s):  
Computer Simulation ◽  
Production System ◽  
Production Systems ◽  
Simulation Method ◽  
System Throughput ◽  
Buffer Allocation ◽  
Simulation Experiments ◽  
Buffer Capacities ◽  
The Relationship ◽  
Support Decision Making

Abstract This paper proposes the application of computer simulation methods to support decision making regarding intermediate buffer allocations in a series-parallel production line. The simulation model of the production system is based on a real example of a manufacturing company working in the automotive industry. Simulation experiments were conducted for different allocations of buffer capacities and different numbers of employees. The production system consists of three technological operations with intermediate buffers between each operation. The technological operations are carried out using machines and every machine can be operated by one worker. Multi-work in the production system is available (one operator operates several machines). On the basis of the simulation experiments, the relationship between system throughput, buffer allocation and the number of employees is analyzed. Increasing the buffer capacity results in an increase in the average product lifespan. Therefore, in the article a new index is proposed that includes the throughput of the manufacturing system and product life span. Simulation experiments were performed for different configurations of technological operations.

scholarly journals SCHEDULING IN A SINGLE-SERVER QUEUE WITH STATE-DEPENDENT SERVICE RATES

2019 ◽  
Vol 34 (4) ◽  
pp. 507-521
Author(s):  
Urtzi Ayesta ◽  
Balakrishna Prabhu ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Arrival Rate ◽  
Complete Characterization ◽  
Single Server ◽  
Holding Costs ◽  
Release Times ◽  
State Dependent ◽  
Service Rates ◽  
Transient System ◽  
The Cost

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

Throughput properties of a queueing network with distributed dynamic routing and flow control

1996 ◽  
Vol 28 (01) ◽  
pp. 285-307 ◽  
Author(s):  
Leandros Tassiulas ◽  
Anthony Ephremides
Keyword(s):  
Flow Control ◽  
Rate Control ◽  
Queueing Network ◽  
Local State ◽  
Service Rate ◽  
Maximum Throughput ◽  
State Information ◽  
Arbitrary Topology ◽  
State Dependent ◽  
Service Rates

A queueing network with arbitrary topology, state dependent routing and flow control is considered. Customers may enter the network at any queue and they are routed through it until they reach certain queues from which they may leave the system. The routing is based on local state information. The service rate of a server is controlled based on local state information as well. A distributed policy for routing and service rate control is identified that achieves maximum throughput. The policy can be implemented without knowledge of the arrival and service rates. The importance of flow control is demonstrated by showing that, in certain networks, if the servers cannot be forced to idle, then no maximum throughput policy exists when the arrival rates are not known. Also a model for exchange of state information among neighboring nodes is presented and the network is studied when the routing is based on delayed state information. A distributed policy is shown to achieve maximum throughput in the case of delayed state information. Finally, some implications for deterministic flow networks are discussed.

Some distributional approximations in Markovian queueing networks

1982 ◽  
Vol 14 (03) ◽  
pp. 654-671 ◽  
Author(s):  
T. C. Brown ◽  
P. K. Pollett
Keyword(s):  
Queueing Networks ◽  
Poisson Processes ◽  
Single Class ◽  
Open Network ◽  
State Dependent ◽  
Service Rates ◽  
Distributional Approximations ◽  
Closed Network ◽  
Poisson Approximations ◽  
Markovian Queueing Networks

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

scholarly journals Service Rate Optimization of Finite Population Queueing Model with State Dependent Arrival and Service Rates

2018 ◽  
Vol 13 (1) ◽  
pp. 60-68
Author(s):  
Sushil Ghimire ◽  
Gyan Bahadur Thapa ◽  
Ram Prasad Ghimire
Keyword(s):  
Finite Population ◽  
Arrival Rate ◽  
Service Rate ◽  
Queueing Model ◽  
State Dependent ◽  
Service Rates ◽  
Rate Optimization

 Providing service immediately after the arrival is rarely been used in practice. But there are some situations for which servers are more than the arrivals and no one has to wait to get served. In this model, arrival rate is

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