On the M/G/1-Queue with Controlled Service Rate

1978 ◽  
pp. 233-239 ◽  
Author(s):  
Manfred Schäl
Keyword(s):  
Service Rate

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

Limitation of Erlang B Traffic Model in Elastic Optical Network for Blocking Probability Estimation

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Ujjwal ◽  
Jaisingh Thangaraj
Keyword(s):  
Blocking Probability ◽  
Optical Network ◽  
Constant Load ◽  
Traffic Model ◽  
Service Rate ◽  
Service Provisioning ◽  
Connection Request ◽  
Elastic Optical Network ◽  
Simulation Results ◽  
Single Path

Abstract In this paper, an algorithm for multipath connection provisioning in elastic optical network (EON) has been proposed. Initially, the algorithm prefers the single-path routing for service provisioning. But when single-path routing is not adequate to serve a dynamic connection, the algorithm switches to the connection request fragmentation. Its computation is based on the parameters such as capacity_constant and capacity_allowed to fragment the connection request on disjoint paths. Simulation results clearly state that the proposed algorithm performs well in service provisioning as compared to the traditional single-path routing algorithms and improves the average network throughput. Thereafter, we have investigated the limitation of Erlang B traffic model in EON for calculation of link blocking probability using routing and spectrum assignment (RSA) algorithm. It is verified by the following two ways: (i) effect on the blocking probability in case of constant load and (ii) effect of slot width on the blocking probability. Our simulation results indicate that in EON due to dynamic RSA, blocking probability is not constant in case of proportionate varying of call arrival and service rate giving constant load and blocking probability depends on the number of slots per link, but in Erlang B traffic model blocking probability is always constant in case of constant load and it considers wavelength per link instead of slots per link. This is attributed to the fact that Erlang B traffic model fails to calculate blocking probability accurately in EON. We have computed the carried traffic on 14 nodes, 21-link National Science Foundation Network (NSFNET) topology.

scholarly journals Stability and moment bounds under utility-maximising service allocations: Finite and infinite networks

2020 ◽  
Vol 52 (2) ◽  
pp. 463-490
Author(s):  
Seva Shneer ◽  
Alexander Stolyar
Keyword(s):  
Steady State ◽  
Wide Class ◽  
Continuous Time ◽  
Service Rate ◽  
Fluid Limit ◽  
Natural Conditions ◽  
Infinite Systems ◽  
Moment Bounds ◽  
Infinite Networks ◽  
State Moment

AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.

A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows

2003 ◽  
Vol 35 (03) ◽  
pp. 793-805 ◽  
Author(s):  
Sem Borst ◽  
Bert Zwart
Keyword(s):  
Service Rate ◽  
Opposite Case ◽  
Peak Rate ◽  
Workload Distribution ◽  
The Mean ◽  
Heavy Tailed ◽  
Insight Into

We determine the exact large-buffer asymptotics for a mixture of light-tailed and heavy-tailed input flows. Earlier studies have found a ‘reduced-load equivalence’ in situations where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is larger than the service rate. In that case, the workload is asymptotically equivalent to that in a reduced system, which consists of a certain ‘dominant’ subset of the heavy-tailed flows, with the service rate reduced by the mean rate of all other flows. In the present paper, we focus on the opposite case where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is smaller than the service rate. Under mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a somewhat ‘dual’ reduced system, multiplied by a certain prefactor. The reduced system now consists of only the light-tailed flows, with the service rate reduced by the peak rate of the heavy-tailed flows. The prefactor represents the probability that the heavy-tailed flows have sent at their peak rate for more than a certain amount of time, which may be interpreted as the ‘time to overflow’ for the light-tailed flows in the reduced system. The results provide crucial insight into the typical overflow scenario.

INFORMATION AND UNCERTAINTY IN A QUEUING SYSTEM

2007 ◽  
Vol 21 (3) ◽  
pp. 361-380 ◽  
Author(s):  
Refael Hassin
Keyword(s):  
Service Quality ◽  
Random Variables ◽  
Random Variable ◽  
Queuing System ◽  
Service Rate ◽  
Single Server ◽  
Profit Function

This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.

Characterization of Manufacturing System Computer Simulation using Taguchi Method

2015 ◽  
Vol 72 (4) ◽  
Author(s):  
Seyed Mojib Zahraee ◽  
Ali Chegeni ◽  
Jafri Mohd Rohani
Keyword(s):  
Computer Simulation ◽  
Taguchi Method ◽  
Manufacturing Industry ◽  
Waiting Times ◽  
Inspection Time ◽  
Total Output ◽  
Service Rate ◽  
Manufacturing Line

In the manufacturing industry, managers and engineers are trying to sustain their competitiveness by achieving high output and productivity. There are some common problems such as waiting times, failures, reworks in production line that impose extra cost to the companies. Therefore, companies are striving to find methods in order to determine and deal with problems using different methods such as mathematical, statistical and computer simulation. The goal of this paper is to increase the total output production and to improve productivity using computer simulation and Taguchi method. This paper introduces a color manufacturing line as a case study which is simulated using arena 13.9 software. Following that the Taguchi method is applied to assess the effect of controllable and uncontrollable factors on the total output production. According to the result of JMP 10 software to conduct Taguchi experiment, the maximum desirability of productivity will be achieved when the value of factors such service rate of delpak machine=UNIF (30, 40), number of labor=14, inspection time=120 and number of Permil=5. Taguchi Method plays an efficient and suitable role in the process improvement, proposing adjustments that will provide an improvement in the productivity. 

scholarly journals Perturbation analysis of a variable M/M/1 queue: a probabilistic approach

2006 ◽  
Vol 38 (01) ◽  
pp. 263-283 ◽  
Author(s):  
Nelson Antunes ◽  
Christine Fricker ◽  
Fabrice Guillemin ◽  
Philippe Robert
Keyword(s):  
Power Series ◽  
Busy Period ◽  
Stationary Process ◽  
Probabilistic Approach ◽  
Power Series Expansion ◽  
Mean Value ◽  
Service Rate ◽  
The Mean ◽  
The Impact ◽  
Period Duration

In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.

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.

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