Throughput maximization in a loss queueing system with heterogeneous servers

1990 ◽  
Vol 27 (03) ◽  
pp. 693-700 ◽  
Author(s):  
Matthew J. Sobel
Keyword(s):  
Queueing System ◽  
Blocking Probability ◽  
Cost Structure ◽  
Throughput Maximization ◽  
Queueing Model ◽  
Heterogeneous Servers ◽  
Waiting Room ◽  
Discounted Cost ◽  
Long Run ◽  
Poisson Arrivals

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

Throughput maximization in a loss queueing system with heterogeneous servers

1990 ◽  
Vol 27 (3) ◽  
pp. 693-700 ◽  
Author(s):  
Matthew J. Sobel
Keyword(s):  
Queueing System ◽  
Blocking Probability ◽  
Cost Structure ◽  
Throughput Maximization ◽  
Queueing Model ◽  
Heterogeneous Servers ◽  
Waiting Room ◽  
Discounted Cost ◽  
Long Run ◽  
Poisson Arrivals

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

Adaptation of the service capacity in a queueing system which is subjected to a change in the arrival rate at unknown epoch

1978 ◽  
Vol 10 (3) ◽  
pp. 666-681 ◽  
Author(s):  
M. Yadin ◽  
S. Zacks
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Arrival Rate ◽  
Cost Structure ◽  
Service Capacity ◽  
Service Intensity ◽  
Discounted Cost ◽  
Adaptation Policies ◽  
The Cost ◽  
Optimal Adaptation

The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.

A martingale approach to the slow server problem

1991 ◽  
Vol 28 (2) ◽  
pp. 480-486 ◽  
Author(s):  
Richard H. Stockbridge
Keyword(s):  
Linear Programming ◽  
Queueing System ◽  
Direct Proof ◽  
Problem Analysis ◽  
Heterogeneous Servers ◽  
Martingale Approach ◽  
Long Run ◽  
Average Criterion ◽  
Server Problem ◽  
Markov Policy

A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.

Some extensions of Takács's limit theorems

1974 ◽  
Vol 11 (4) ◽  
pp. 752-761 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Limit Theorems ◽  
Queueing System ◽  
Waiting Times ◽  
Interarrival Time ◽  
Positive Probability ◽  
Limiting Distributions ◽  
Waiting Room ◽  
Poisson Arrivals

In this paper, we establish that if an interarrival time exceeds a service time with a positive probability then the queueing system GI/G/s with a finite waiting room always has proper limiting distributions for its characteristics such as queue length, waiting time and the remaining service times of the customers being served. The result remains valid if we consider a GI/G/s system with bounded waiting times. A technique is also given to establish that for a system with Poisson arrivals the limiting distributions of the queueing characteristics at an epoch of arrival and at an arbitrary epoch are identical.

Some extensions of Takács's limit theorems

1974 ◽  
Vol 11 (04) ◽  
pp. 752-761
Author(s):  
D. N. Shanbhag
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Limit Theorems ◽  
Queueing System ◽  
Waiting Times ◽  
Interarrival Time ◽  
Positive Probability ◽  
Limiting Distributions ◽  
Waiting Room ◽  
Poisson Arrivals

In this paper, we establish that if an interarrival time exceeds a service time with a positive probability then the queueing system GI/G/s with a finite waiting room always has proper limiting distributions for its characteristics such as queue length, waiting time and the remaining service times of the customers being served. The result remains valid if we consider a GI/G/s system with bounded waiting times. A technique is also given to establish that for a system with Poisson arrivals the limiting distributions of the queueing characteristics at an epoch of arrival and at an arbitrary epoch are identical.

A martingale approach to the slow server problem

1991 ◽  
Vol 28 (02) ◽  
pp. 480-486 ◽  
Author(s):  
Richard H. Stockbridge
Keyword(s):  
Linear Programming ◽  
Queueing System ◽  
Direct Proof ◽  
Problem Analysis ◽  
Heterogeneous Servers ◽  
Martingale Approach ◽  
Long Run ◽  
Average Criterion ◽  
Server Problem ◽  
Markov Policy

A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.

Adaptation of the service capacity in a queueing system which is subjected to a change in the arrival rate at unknown epoch

1978 ◽  
Vol 10 (03) ◽  
pp. 666-681 ◽  
Author(s):  
M. Yadin ◽  
S. Zacks
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Arrival Rate ◽  
Cost Structure ◽  
Service Capacity ◽  
Service Intensity ◽  
Discounted Cost ◽  
Adaptation Policies ◽  
The Cost ◽  
Optimal Adaptation

The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 &lt; μ2 &lt; · · · &lt; μ N . The cost structure consists of the cost changing μ i to μ j (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.

scholarly journals An M /M /1 Queueing System with Server on Attacks and Repair

2019 ◽  
Vol 9 (2) ◽  
pp. 2616-2621
Keyword(s):  
Communication System ◽  
System Performance ◽  
Queueing System ◽  
Random Variable ◽  
Repair Time ◽  
Time Interval ◽  
Queueing Model ◽  
Numerical Illustration ◽  
Work Station ◽  
Long Run

We consider a M M/ /1 queueing model of a communication system subject to random attacks on service station. In such attack system, the time interval between any two attacks is an exponentially distributed random variable with mean1/  . When the server fails by an attack, any customer getting service at that time becomes damaged. The failed server is immediately taken for repair and the damaged customer is washed out. Customers in the queue waiting for service are not washed out. The repair time of the server undergoing repair is assumed to be an exponentially distributed random variable with mean1/ . During repair time, the customers are allowed to wait for service maintain First Come First Served order. After the completion of repair, the server returns to the work-station immediately without any delay, even if there is no customer to render service. We derive explicit form of the state probabilities of the attack system in the long run. We also obtain measures of system performance and the model is validated by a numerical illustration.

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

scholarly journals Performance Evaluation of Cloud Data Centers with Batch Task Arrivals

2013 ◽  
pp. 199-223 ◽  
Author(s):  
Hamzeh Khazaei ◽  
Jelena Mišić ◽  
Vojislav B. Mišić
Keyword(s):  
Performance Evaluation ◽  
Queue Length ◽  
Blocking Probability ◽  
General Distribution ◽  
Cloud Data ◽  
Wide Range ◽  
Accurate Performance ◽  
Cloud Data Centers ◽  
Poisson Arrivals

Accurate performance evaluation of cloud computing resources is a necessary prerequisite for ensuring that Quality of Service (QoS) parameters remain within agreed limits. In this chapter, the authors consider cloud centers with Poisson arrivals of batch task requests under total rejection policy; task service times are assumed to follow a general distribution. They describe a new approximate analytical model for performance evaluation of such systems and show that important performance indicators such as mean request response time, waiting time in the queue, queue length, blocking probability, probability of immediate service, and probability distribution of the number of tasks in the system can be obtained in a wide range of input parameters.

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