Discrete-time queues with generally distributed service times and renewal-type server interruptions

Fiems, Dieter; Steyaert, Bart; Bruneel, Herwig

doi:10.1016/j.peva.2003.08.004

Cited by 41 publications

(38 citation statements)

References 14 publications

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“…Using the formula we obtained earlier for the pgf V (·) in equation (16), the above result translates into the following explicit expression for the pgf of the queueing delay:…”

Section: Analysis Of the Delaymentioning

confidence: 84%

Discrete-time queues with variable service capacity: a basic model and its analysis

et al. 2013

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In this paper, we present a basic discrete-time queueing model whereby the service process is decomposed in two (variable) components: the demand of each customer, expressed in a number of work units needed to provide full service of the customer, and the capacity of the server, i.e., the number of work units that the service facility is able to perform per time unit. The model is closely related to multi-server queueing models with server interruptions, in the sense that the service facility is able to deliver more than one unit of work per time unit, and that the number of work units that can be executed per time unit is not constant over time.Although multi-server queueing models with server interruptions -to some extentallow us to study the concept of variable capacity, these models have a major disadvantage. The models are notoriously hard to analyze and even when explicit expressions are obtained, these contain various unknown probabilities that have to be calculated numerically, which makes the expressions difficult to interpret. For the model in this paper, on the other hand, we are able to obtain explicit closed-form expressions for the main performance measures of interest. Possible applications of this type of queueing model are numerous: the variable service capacity could model variable available bandwidths in communication networks, a varying production capacity in factories, a variable number of workers in an HR-environment, varying capacity in road traffic, etc.

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“…Using the formula we obtained earlier for the pgf V (·) in equation (16), the above result translates into the following explicit expression for the pgf of the queueing delay:…”

Section: Analysis Of the Delaymentioning

confidence: 84%

Discrete-time queues with variable service capacity: a basic model and its analysis

et al. 2013

Self Cite

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“…So, if the k-th and (k + 1)-st arriving customers arrive at the same epoch, the (k + 1)-st customer sees the k-th customer as part of the buffer occupancy upon arrival, while the opposite is not true. Since we therefore look at the buffer occupancy as left by departing customers and as seen by arriving customers (rather than at arrival and departure epochs), we can regard the system as a single-arrival, single-departure system (see [14] for a similar observation). For this type of systems, it holds that buffer occupancies as seen by departing and arriving customers are identically distributed (see [15]), and thusB…”

Section: Immediate Accessmentioning

confidence: 99%

The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited

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Bruneel

Claeys

et al. 2013

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. We analyze a discrete-time queue with variable service capacity, such that the total amount of work that can be performed during each time slot is a stochastic variable that is geometrically distributed. We study the buffer occupancy by constructing an analogous model with fixed service capacity. In contrast with classical discrete-time queueing models, however, the service times in the fixed-capacity model can take the value zero with positive probability (service times are non-negative). We study the late arrival models with immediate and delayed access, the first model being the most natural model for a system with fixed capacity and non-negative service times and the second model the more practically relevant model for the variable-capacity model.

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“…Finally, an unslotted optical MAN (Metropolitan Area Network) ring operating with asynchronous variable length optical packets is modeled as a PRI priority queue in [8]. In [1,9,10], discrete-time queues with a preemptive repeat priority scheduling discipline are studied. A preemptive repeat protocol for voice-data integration in a ring-based LAN is studied in [9].…”

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confidence: 99%

“…Note that the data and voice queues are all analyzed separately and that the queueing model for the low-priority queue is given by a queueing model with service interruptions. In [10], preemptive priority queues are studied. This is also done by means of queues with service interruptions.…”

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The discrete-time preemptive repeat identical priority queue

2006

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Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discretetime two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed service times. Newly arriving high-priority customers interrupt the on-going service of a low-priority customer. After all high-priority customers have left the system, the interrupted service of the low-priority customer has to be repeated completely. By means of a probability generating functions approach, we analyze the system content and the delay of both types of customers. Performance measures (such as means and variances) are calculated and the impact of the priority scheduling is discussed by means of some numerical examples.

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Discrete-time queues with generally distributed service times and renewal-type server interruptions

Cited by 41 publications

References 14 publications

Discrete-time queues with variable service capacity: a basic model and its analysis

Discrete-time queues with variable service capacity: a basic model and its analysis

The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited

The discrete-time preemptive repeat identical priority queue

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