A Taylor series expansions approach to queues with train arrivals

Turck, Koen De; Fiems, Dieter; Wittevrongel, Sabine; Bruneel, Herwig

doi:10.4108/icst.valuetools.2011.245768

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…For such a model with gaps, the analysis becomes much harder than for the train arrival model we considered in our paper [1]. For instance, in [8] a FIFO queue with gaps in the arriving trains is approximately analyzed through the use of Taylor series approximations. Extension of this approach to priority queueing models would be an interesting and challenging research topic.…”

Section: Further Extensions Of the Queueing Analysismentioning

confidence: 99%

Rejoinder on: Queueing models for the analysis of communication systems

Bruneel

Fiems

Walraevens

et al. 2014

TOP

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First of all, we want to express our gratitude to the former Editor-in-Chief of the journal TOP, our fondly-remembered colleague Professor Jesús Artalejo, who invited us about one year ago to write a review paper for TOP on the topic of queueing models for the analysis of communication systems. Also, we want to thank the three discussants for the effort of carefully reading our paper and adding interesting information. We mention in particular the insightful discussion of Onno Boxma on the role of transform methods in queueing analysis, their strengths and weaknesses. With respect to scheduling disciplines, Onno Boxma also adds the topic of dynamic priority scheduling schemes. As far as traffic modeling is concerned, Alexander Dudin not only refers to the well-known D-BMAP model as an alternative description of bursty, correlated traffic streams, but he also points to several related papers on continuous-time models with session-based arrivals. Harry Perros emphasizes the practical applications of discrete-time queueing models in the performance evaluation of various subsystems of modern telecommunication networks. In particular, he discusses the restriction introduced by the assumption in our paper that packets be of fixed length, which makes the results applicable in the context of ATM, in optical burst switching, and in HTTP adaptive video streaming, but not in a general IP network where packets typically are of variable length.A very striking observation is that all three discussants explicitly comment on the use of discrete-time queueing models in much of our work of the last thirty years (including the current paper), as opposed to the much more frequently encountered continuous-time models in literature. As these remarks are of a very generic nature, we isolate this topic from the more specific comments in this rejoinder. Therefore, our responses are structured around two main topics: (1) the aspect of modeling and queueing analysis in the discrete time domain and (2) possible extensions of and remarks on our presented analysis of the two-class priority queue with train arrivals. * SMACS: Stochastic Modeling and Analysis of Communication Systems

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Section: Further Extensions Of the Queueing Analysismentioning

confidence: 99%

Rejoinder on: Queueing models for the analysis of communication systems

Bruneel

Fiems

Walraevens

et al. 2014

TOP

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“…Therefore, we believe that this solution technique can be useful for more advanced queueing models with customer impatience. Note that the approach with power series in a parameter other than the load has also proven to be useful in other types of queueing models, e.g., a Generalized Processor Sharing model [35] and a model with train arrivals [11].…”

Section: Introductionmentioning

confidence: 99%

A discrete-time queue with customers with geometric deadlines

Bruneel

Maertens

2015

Performance Evaluation

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This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. More specifically, we model the deadlines of the consecutive customers as independent and geometrically distributed random variables. Customers enter the system according to a general independent arrival process, i.e., the numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. Service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for such quantities as the generating function and the expected value of the system content, the mean customer delay and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures, based on a polynomial approximation technique. We believe this technique, in its own right, is also one of the major (methodological) contributions of the paper.Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc.

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A functional approximation for retrial queues with two way communication

Ouazine

Abbas

2015

Ann Oper Res

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A Taylor series expansions approach to queues with train arrivals

Cited by 5 publications

References 14 publications

Rejoinder on: Queueing models for the analysis of communication systems

Rejoinder on: Queueing models for the analysis of communication systems

A discrete-time queue with customers with geometric deadlines

A functional approximation for retrial queues with two way communication

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