12 research outputs found
Π‘ΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΡΠ΅ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΠ°Π½Π°Π»ΡΠ½ΠΎΠΉ Π½Π΅ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Ρ FCFS ΠΎΡΠ±ΠΈΡΠΎΠΉ ΠΈ ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΡΠΌ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ΠΌ
In the paper we deal with a Markovian queueing system with heterogeneous servers and constant retrial rate. The system operates under a threshold policy. The system is described by quasi-birth-and-death process with infinitesimal matrix depending on the threshold levels. Using a matrix-geometric approach we perform a stationary analysis of the system, derive expressions for the mean performance measures and formulas for optimal threshold levels.Π ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠ°ΡΠΊΠΎΠ²ΡΠΊΠ°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° ΠΌΠ°ΡΡΠΎΠ²ΠΎΠ³ΠΎ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ Ρ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΠΌΠΈ Π½Π΅ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΡΠΌΠΈ ΠΏΡΠΈΠ±ΠΎΡΠ°ΠΌΠΈ. ΠΠΊΠ»ΡΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠΈΠ±ΠΎΡΠΎΠ² ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡΡ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ°ΡΠ²ΠΊΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ Π½Π΅ ΠΏΠΎΠ»ΡΡΠΈΠ»ΠΈ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ, Π½Π°ΠΏΡΠ°Π²Π»ΡΡΡΡΡ Π½Π° ΠΎΡΠ±ΠΈΡΡ, Π³Π΄Π΅ ΠΎΠ½ΠΈ ΡΠ΅ΡΠ΅Π· ΡΠ»ΡΡΠ°ΠΉΠ½ΠΎΠ΅ Π²ΡΠ΅ΠΌΡ ΠΏΠΎΠ²ΡΠΎΡΡΡΡ ΠΏΠΎΠΏΡΡΠΊΡ Π·Π°Π½ΡΡΡ ΠΏΡΠΈΠ±ΠΎΡ. ΠΠ°ΡΠ²ΠΊΠΈ Π½Π° ΠΎΡΠ±ΠΈΡΠ΅ ΡΠΎΡΠΌΠΈΡΡΡΡ ΠΎΡΠ΅ΡΠ΅Π΄Ρ Ρ FCFS Π΄ΠΈΡΡΠΈΠΏΠ»ΠΈΠ½ΠΎΠΉ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ. Π‘ΠΈΡΡΠ΅ΠΌΠ° ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ ΠΎΠ±ΠΎΠ±ΡΡΠ½Π½ΡΠΌ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠΌ ΡΠ°Π·ΠΌΠ½ΠΎΠΆΠ΅Π½ΠΈΡ ΠΈ Π³ΠΈΠ±Π΅Π»ΠΈ Ρ Π±ΠΎΠ»ΡΡΠΈΠΌ ΡΠΈΡΠ»ΠΎΠΌ ΠΏΠΎΠ³ΡΠ°Π½ΠΈΡΠ½ΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· ΡΠΈΡΡΠ΅ΠΌΡ Π² ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΡΠ΅ΠΆΠΈΠΌΠ΅, Π²ΡΠ²ΠΎΠ΄ΡΡΡΡ ΠΌΠ°ΡΡΠΈΡΠ½ΡΠ΅ Π²ΡΡΠ°ΠΆΠ΅Π½ΠΈΡ Π΄Π»Ρ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡ ΡΡΠ΅Π΄Π½ΠΈΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΎΡΠΌΡΠ»Ρ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΡΡ
ΡΡΠΎΠ²Π½Π΅ΠΉ
Π Π°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΎΠΆΠΈΠ΄Π°Π½ΠΈΡ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ Ρ FCFS ΠΎΡΠ±ΠΈΡΠΎΠΉ ΠΈ ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΡΠΌ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ΠΌ
We perform a waiting time analysis of a retrial queue with several heterogeneous servers and threshold control policy. The blocked customers are dispatched to the infinitely large orbit with FCFS service discipline. The system is analyzed in steady-state by deriving expressions for the Laplace transforms of the waiting time, the probability generating functions for the number of retrials made by a customer and for various moments of corresponding quantities. Some illustrative numerical examples and their discussion are presented.ΠΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΎΠΆΠΈΠ΄Π°Π½ΠΈΡ Π² ΠΌΠ°ΡΠΊΠΎΠ²ΡΠΊΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠ΅ Ρ ΠΏΠΎΠ²ΡΠΎΡΠ½ΡΠΌΠΈ Π·Π°ΡΠ²ΠΊΠ°ΠΌΠΈ, Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΠΌΠΈ Π½Π΅ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΡΠΌΠΈ ΠΏΡΠΈΠ±ΠΎΡΠ°ΠΌΠΈ ΠΈ ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ»ΠΎΠΊΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ Π·Π°ΡΠ²ΠΊΠΈ ΠΎΠΆΠΈΠ΄Π°ΡΡ ΡΠ²ΠΎΠ΅ΠΉ ΠΎΡΠ΅ΡΠ΅Π΄ΠΈ Π½Π° ΠΎΡΠ±ΠΈΡΠ΅ Π±Π΅ΡΠΊΠΎΠ½Π΅ΡΠ½ΠΎΠΉ ΡΠΌΠΊΠΎΡΡΠΈ Ρ FCFS Π΄ΠΈΡΡΠΈΠΏΠ»ΠΈΠ½ΠΎΠΉ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ. Π‘ΠΈΡΡΠ΅ΠΌΠ° ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΡΡΡ Π² ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΡΠ΅ΠΆΠΈΠΌΠ΅. ΠΡΠ²ΠΎΠ΄ΡΡΡΡ Π²ΡΡΠ°ΠΆΠ΅Π½ΠΈΡ Π΄Π»Ρ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ ΠΠ°ΠΏΠ»Π°ΡΠ° Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΎΠΆΠΈΠ΄Π°Π½ΠΈΡ, ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠΈΡ
ΡΡΠ½ΠΊΡΠΈΠΉ ΡΠΈΡΠ»Π° ΠΏΠΎΠ²ΡΠΎΡΠ½ΡΡ
ΠΏΠΎΠΏΡΡΠΎΠΊ Π΄ΠΎ ΠΌΠΎΠΌΠ΅Π½ΡΠ° ΠΏΠΎΡΡΡΠΏΠ»Π΅Π½ΠΈΡ Π½Π° ΠΏΡΠΈΠ±ΠΎΡ, Π° ΡΠ°ΠΊΠΆΠ΅ Π΄Π»Ρ ΠΌΠΎΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌΡΡ
Π²Π΅Π»ΠΈΡΠΈΠ½. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΠ΅ ΠΏΡΠΈΠΌΠ΅ΡΡ Ρ ΠΈΠ»Π»ΡΡΡΡΠ°ΡΠΈΡΠΌΠΈ ΠΈ ΠΈΡ
ΠΎΠ±ΡΡΠΆΠ΄Π΅Π½ΠΈΠ΅
To analysis of a two-buffer queuing system with cross-type service and additional penalties
The concept of cloud computing was created to better preserve user privacy and data storage security. However, the resources allocated for processing this data must be optimally allocated. The problem of optimal resource management in the loud computing environment is described in many scientific publications. To solve the problems of optimality of the distribution of resources of systems, you can use the construction and analysis of QS. We conduct an analysis of two-buffer queuing system with cross-type service and additional penalties, based on the literature reviewed in the article. This allows us to assess how suitable the model presented in the article is for application to cloud computing. For a given system different options for selecting applications from queues are possible, queue numbers, therefore, the intensities of transitions between the states of the system will change. For this, the system has a choice policy that allows the system to decide how to behave depending on its state. There are four components of such selection management models, which is a stationary policy for selecting a queue number to service a ticket on a vacated virtual machine each time immediately before service ends. A simulation model was built for numerical analysis. The results obtained indicate that requests are practically not delayed in the queue of the presented QS, and therefore the policy for a given model can be considered optimal. Although Poisson flow is the simplest for simulation, it is quite acceptable for performance evaluation. In the future, it is planned to conduct several more experiments for different values of the intensity of requests and various types of incoming flows.ΠΠΎΠ½ΡΠ΅ΠΏΡΠΈΡ ΠΎΠ±Π»Π°ΡΠ½ΡΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ Π±ΡΠ»Π° ΡΠΎΠ·Π΄Π°Π½Π° Π΄Π»Ρ ΡΠ»ΡΡΡΠ΅Π½ΠΈΡ ΠΊΠΎΠ½ΡΠΈΠ΄Π΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΡΡΠΈ ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ ΠΈ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
. ΠΠ΄Π½Π°ΠΊΠΎ ΡΠ΅ΡΡΡΡΡ, Π²ΡΠ΄Π΅Π»ΡΠ΅ΠΌΡΠ΅ Π΄Π»Ρ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΡΡΠΈΡ
Π΄Π°Π½Π½ΡΡ
, Π΄ΠΎΠ»ΠΆΠ½Ρ Π±ΡΡΡ ΠΏΡΠ°Π²ΠΈΠ»ΡΠ½ΠΎ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ. ΠΡΠΎΠ±Π»Π΅ΠΌΠ° ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ Π² ΡΡΠ΅Π΄Π΅ ΠΎΠ±Π»Π°ΡΠ½ΡΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ ΠΎΠΏΠΈΡΠ°Π½Π° Π²ΠΎ ΠΌΠ½ΠΎΠ³ΠΈΡ
Π½Π°ΡΡΠ½ΡΡ
ΠΏΡΠ±Π»ΠΈΠΊΠ°ΡΠΈΡΡ
. ΠΠ»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΡΡΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅ΡΡΡΡΠΎΠ² ΡΠΈΡΡΠ΅ΠΌ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΠ΅ ΠΈ Π°Π½Π°Π»ΠΈΠ· Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ Π‘ΠΠ. ΠΠ²ΡΠΎΡΠ°ΠΌΠΈ ΠΏΡΠΎΠ²Π΅Π΄ΡΠ½ Π°Π½Π°Π»ΠΈΠ· ΡΠΈΡΡΠ΅ΠΌΡ ΠΌΠ°ΡΡΠΎΠ²ΠΎΠ³ΠΎ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ Ρ Π΄Π²ΡΠΌΡ ΠΎΡΠ΅ΡΠ΅Π΄ΡΠΌΠΈ Ρ ΠΊΡΠΎΡΡ-ΡΠΈΠΏΠΎΠΌ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ ΠΈ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΡΡΠ°ΡΠ°ΠΌΠΈ, ΠΊΠΎΡΠΎΡΡΠΉ ΠΎΡΠ½ΠΎΠ²ΡΠ²Π°Π΅ΡΡΡ Π½Π° Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ½ΡΡ
ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°Ρ
, ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Π½ΡΡ
Π² ΡΡΠ°ΡΡΠ΅. ΠΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π°ΠΌ ΠΎΡΠ΅Π½ΠΈΡΡ, Π½Π°ΡΠΊΠΎΠ»ΡΠΊΠΎ ΠΌΠΎΠ΄Π΅Π»Ρ, ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π½Π°Ρ Π² ΡΡΠ°ΡΡΠ΅, ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΈΡ Π΄Π»Ρ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ Π² ΠΎΠ±Π»Π°ΡΠ½ΡΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡΡ
. ΠΠ°Π½Π½Π°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° ΠΏΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ ΡΠ°Π·Π½ΡΠ΅ Π²Π°ΡΠΈΠ°Π½ΡΡ Π²ΡΠ±ΠΎΡΠ° Π·Π°ΡΠ²ΠΎΠΊ ΠΈΠ· ΠΎΡΠ΅ΡΠ΅Π΄Π΅ΠΉ, Π½ΠΎΠΌΠ΅ΡΠΎΠ² ΠΎΡΠ΅ΡΠ΅Π΄Π΅ΠΉ, ΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎ, ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄ΠΎΠ² ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΡΡΠΎΡΠ½ΠΈΡΠΌΠΈ ΡΠΈΡΡΠ΅ΠΌΡ Π±ΡΠ΄ΡΡ ΠΌΠ΅Π½ΡΡΡΡΡ. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ° Π²ΡΠ±ΠΎΡΠ°, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΠΈΡΡΠ΅ΠΌΠ΅ ΡΠ΅ΡΠ°ΡΡ, ΠΊΠ°ΠΊ ΡΠ΅Π±Ρ Π²Π΅ΡΡΠΈ Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΡΠ²ΠΎΠ΅Π³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ. ΠΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΡΠ΅ΡΡΡΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²ΡΠ±ΠΎΡΠΎΠΌ, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡ ΡΠΎΠ±ΠΎΠΉ ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΡΡ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΡ Π΄Π»Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π½ΠΎΠΌΠ΅ΡΠ° ΠΎΡΠ΅ΡΠ΅Π΄ΠΈ, ΠΈΠ· ΠΊΠΎΡΠΎΡΠΎΠΉ Π±ΡΠ΄Π΅Ρ Π²Π·ΡΡΠ° Π·Π°ΡΠ²ΠΊΠ° Π½Π° ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΠ΅. ΠΠ°Π½Π½ΡΠΉ Π²ΡΠ±ΠΎΡ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΊΠ°ΠΆΠ΄ΡΠΉ ΡΠ°Π· Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎ ΠΏΠ΅ΡΠ΅Π΄ ΠΎΠΊΠΎΠ½ΡΠ°Π½ΠΈΠ΅ΠΌ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ. ΠΠ»Ρ ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΏΠΎΡΡΡΠΎΠ΅Π½Π° ΠΈΠΌΠΈΡΠ°ΡΠΈΠΎΠ½Π½Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ
Analysis of the busy period in threshold control system
Consideration was given to the controllable Markov queuing system with nonhomogeneous servers and threshold policy of server activation depending on the queue length. By the busy period is meant the time interval between the instant of customer arrival to the empty system and the instant of service completion when the system again becomes free. The system busy period and the number of serviced customers were analyzed. Recurrent relations for the distribution density in terms of the Laplace transform and generating function, as well as formulas for calculation of the corresponding arbitrary-order moments, were obtained. Β© 2010 Pleiades Publishing, Ltd
Analysis of the busy period in threshold control system
Consideration was given to the controllable Markov queuing system with nonhomogeneous servers and threshold policy of server activation depending on the queue length. By the busy period is meant the time interval between the instant of customer arrival to the empty system and the instant of service completion when the system again becomes free. The system busy period and the number of serviced customers were analyzed. Recurrent relations for the distribution density in terms of the Laplace transform and generating function, as well as formulas for calculation of the corresponding arbitrary-order moments, were obtained. Β© 2010 Pleiades Publishing, Ltd
Numerical analysis of optimal control for system with nonuniform units
For construction of the optimal service disciplines, different numerical methods of the Howard iterative algorithm type are often used. However because of usually high dimensionality of real problems, direct application of such the calculation approaches is often not efficient. With the help of the known Howard algorithm, numerical study is carried out of optimal service disciplines by a system with several nonuniform devices with respect to the minimization criterion of average stationary demands number in the system
Numerical analysis of optimal control for system with nonuniform units
For construction of the optimal service disciplines, different numerical methods of the Howard iterative algorithm type are often used. However because of usually high dimensionality of real problems, direct application of such the calculation approaches is often not efficient. With the help of the known Howard algorithm, numerical study is carried out of optimal service disciplines by a system with several nonuniform devices with respect to the minimization criterion of average stationary demands number in the system
Numerical Study of the Optimal Control of a System with Heterogeneous Servers
For a system with several heterogeneous servers, the well-known Howard algorithm was used to study numerically whether the optimal servicing disciplines satisfy the criterion for minimum stationary number of customers in system
On the slow server problem
In this paper the problem of optimal control over a Markov queueing system with heterogeneous servers and a joint queue is considered, which is also known in the literature as "the slow server problem." The classical model is generalized here to the case with delay and call serving penalties. It is proved here that the optimal control policy for servers' activating is of monotonic and threshold nature. Β© 2009 Pleiades Publishing, Ltd
On the slow server problem
In this paper the problem of optimal control over a Markov queueing system with heterogeneous servers and a joint queue is considered, which is also known in the literature as "the slow server problem." The classical model is generalized here to the case with delay and call serving penalties. It is proved here that the optimal control policy for servers' activating is of monotonic and threshold nature. Β© 2009 Pleiades Publishing, Ltd