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This is the PREFACE to the Special Issue "Queueing-inventory: analytical and simulation modeling and classical and retrial queues and inventory". The year 2022 was the 30th anniversary of Queueing-inventory. It was in that connection that the guest editors requested Professor Endre Boros, the Editor-in-Chief of Annals of Operations Research, for permission to guest edit a special issue. This was granted by the Editorial Board of the journal. [ABSTRACT FROM AUTHOR]

This paper analyses a single server retrial queuing model with service interruptions, resumption/restart of interrupted service. The service is assumed to get interrupted according to a Poisson process. The interrupted service is either resumed or restarted according to the realization of two competing independent, non-identically distributed random variables, the realization times of which follow exponential distributions. Arrival of primary customers constitutes a Poisson process. On arrival if a customer finds an idle server, he is immediately taken for service. If the server is busy when a customer arrives, this customer goes to an orbit of infinite capacity from where he makes repeated attempts for service according to a Poisson process with parameter β. After an unsuccessful retrial he rejoins the orbit with probability p and leaves the system without waiting for service with probability q = 1 − p. The service time durations follow PH distribution with representation ( α, S) of order m, when there is no interruption. The system is found to be always stable if q > 0. The case q = 0 is also analyzed. Using Matrix analytic method, expressions for important system characteristics such as expected service time, expected number of interruptions are obtained. System performance measures are numerically explored and the effect of service interruptions in a retrial set up is studied. [ABSTRACT FROM AUTHOR]

In this paper we consider a single server queueing system to which customers arrive according to a Poisson process, each demanding exactly one unit of the inventoried item. Service time duration is exponentially distributed. Inventory is replenished according to ( s, S) policy, with lead time following exponential distribution. The service may be interrupted according to a Poisson process in which case the service restarts after an exponentially distributed time. Upon arrival if a customer finds the server busy, it leaves the service area to join an orbit and retries for service from there. The interval between two successive repeated attempts is exponentially distributed. We assume that while the server is under interruption an arriving customer joins the system with some probability or leaves for ever with complementary probability. Further it is assumed that while the server is on interruption a retrying customer goes back to the orbit with a certain probability and with complementary probability leaves the system for ever. No arrival or retrial is entertained when the inventory level is zero. We model the above system as a level dependent quasi birth death process (LIQBD). The stability of the system has been studied using matrix analytic method and the steady state vector is obtained applying Neuts-Rao truncation procedure. Several system performance measures, including the waiting time of a customer in the orbit, has been derived and their dependence on different system parameters has been extensively investigated numerically. [ABSTRACT FROM AUTHOR]

An inventory system with two parallel service facilities is considered. A certain number of customers are transferred from longer to shorter queue whenever their difference reaches a prescribed quantity. Along with this customer transfer, a certain quantity of inventory is also transferred, depending on availability. Further, if one of the queues has customers, but has no inventoried items whereas the other has at least one inventoried item to spare, then exactly one item is taken to the former and service begins thereby enhancing the efficiency of the system. Stability of the system is analysed. Several performance measures that helps in efficient design of such systems, are computed. Some numerical results are provided. [ABSTRACT FROM AUTHOR]