A queueing system with inventory and mixed exponentially distributed lead times

Saffari, Mohammad; Haji, Rasoul; Hassanzadeh, Farhad

doi:10.1007/s00170-010-2883-0

Cited by 24 publications

(11 citation statements)

References 10 publications

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“…In a second step, we will show that the results of Saffari et al [27] and of Saffari et al [28] for queueing-inventory systems under (r, Q) policy can be obtained by our method and can even be slightly generalized.…”

Section: Example 7 Krishnamoorthy and Viswanathmentioning

confidence: 85%

“…This shows that the mentioned independence results in [27,28,30,32,37] do not depend on the specific properties of the attached second subsystem. Furthermore, we will show that the theorem can be interpreted as a strong insensitivity property of the system: As long as ergodicity is maintained, the environment can change drastically without changing the steady state distribution of the queue length.…”

Section: Introductionmentioning

confidence: 80%

“…Starting from Example 5, Saffari et al [27] proved that under (r, Q) policy the integrated queueing-inventory M/M/1/∞ system with hyper-exponential lead times (=mixtures of exponential distributions) has product-form equilibrium by solving directly the steady state equations. In [28], Saffari et al generalized this result to general lead time distributions.…”

Section: Example 7 Krishnamoorthy and Viswanathmentioning

confidence: 99%

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Loss systems in a random environment: steady state analysis

Krenzler

Daduna

2014

Queueing Syst

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We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove a product-form steady state distribution of the joint queueingenvironment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, for example, from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, for example, of queueing-inventory processes. We investigate further classical loss systems, where, due to finite waiting room, loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise.Keywords Queueing systems · Random environment · Product form steady state · Loss systems · M/M/1/∞ · M/M/m/∞ · M/M/m/N · Inventory systems · Availability · Lost sales Mathematics Subject Classification Primary 60K · 60J10 · 60F05 · 60K20 · 90B22 · 90B05

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Section: Example 7 Krishnamoorthy and Viswanathmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 80%

Section: Example 7 Krishnamoorthy and Viswanathmentioning

confidence: 99%

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Loss systems in a random environment: steady state analysis

Krenzler

Daduna

2014

Queueing Syst

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“…Cohen [2] notes that although the broad field of applications amply justifies an intensive study of queueing models, it turned out that these models are also of great use outside the field of queueing theory, e.g., in inventory and maintenance theory. Saffari and Haji [3] considered M/M/1 systems with inventory in which completing each service in the queueing system requires an on-hand inventory. Teimoury et al [4] evaluated a service/make-to-order firm with heterogeneous price and delivery time-sensitive customers as an M/M/1 queuing system is analyzed.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sample sizes in an M/M/1 queueing systems

Quinino

Cruz

2016

Int J Adv Manuf Technol

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Although the broad field of applications amply justifies an intensive study of queueing models, it turned out that these models are also of great use outside the field of queueing theory, e.g., in inventory and maintenance theory very important for production systems. In these applications, the queue model M/M/1 has several works that illustrate its importance, but usually, they adopt the parameters known. The literature presents estimation methods such as maximum likelihood and Bayesian that could be directly applied. However, there is no discussion about planning the sample size to guarantee the precision of the parameters that are estimated. An accurate estimate of the model parameters can avoid wrong decisions on inventory control and maintenance. The focus here is on sample size determination for estimates in single-server Markovian infinity queues, considered the simplest and yet most useful queueing model for its accuracy to model many problems of practical interest. In this article, a Bayesian method is described for sample size determination for traffic intensity estimation, one of the most important parameters for performance evaluation of queueing systems. Numerical results are presented to attest to the efficiency and efficacy of the approach.

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“…Classical queue with inventoried items for service is also studied by Saffari et al [14] where the control policy followed 2 Advances in Operations Research is ( , ) and lead time is mixed exponential distribution. Customers arriving during zero inventory are lost forever.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Multiserver Queueing-Inventory System

Krishnamoorthy

Manikandan

Shajin

2015

Advances in Operations Research

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We attempt to derive the steady-state distribution of the / / queueing-inventory system with positive service time. First we analyze the case of = 2 servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the ( , ) policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair ( , ) and the corresponding expected minimum cost are computed. As in the case of / / retrial queue with ≥ 3, we conjecture that / / for ≥ 3, queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutive to transitions of the inventory level (i.e., the first return time to ) is computed. We also obtain several system performance measures.

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A queueing system with inventory and mixed exponentially distributed lead times

Cited by 24 publications

References 10 publications

Loss systems in a random environment: steady state analysis

Loss systems in a random environment: steady state analysis

Bayesian sample sizes in an M/M/1 queueing systems

Analysis of a Multiserver Queueing-Inventory System

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