Queueing System with Potential for Recruiting Secondary Servers

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a G I/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented

Analysis of Single-Server Queue with Phase-Type Service and Energy Harvesting

We propose a queueing model suitable, for example, for modelling operation of nodes of sensor networks. The sensor node senses a random field and generates packets to be transmitted to the central node. The sensor node has a battery of a finite capacity and harvests energy during its operation from outside (using solar cells, wind turbines, piezoelectric cells, etc.). We assume that, generally speaking, service (transmission) of a packet consists of a random number of phases and implementation of each phase requires a unit of energy. If the battery becomes empty, transmission is failed. To reduce the probability of forced transmission termination, we suggest that the packet can be accepted for transmission only when the number of energy units is greater than or equal to some threshold. Under quite general assumptions about the pattern of the arrival processes of packets and energy, we compute the stationary distributions of the system states and the waiting time of a packet in the system and numerically analyze performance measures of the system as functions of the threshold. Validity of Little’s formula and its counterpart is verified

Queueing System with Potential for Recruiting Secondary Servers

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a GI/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented

Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers

We consider a multiserver queueing system with two input flows. Type-1 customers have preemptive priority and are lost during arrival only if all servers are occupied by type-1 customers. If all servers are occupied, but some provide service to type-2 customers, service of type-2 customer is terminated and type-1 customer occupies the server. If the number of busy servers is less than the threshold M during type-2 customer arrival epoch, this customer is accepted. Otherwise, it is lost or becomes a retrial customer. It will retry to obtain service. Type-2 customer whose service is terminated is lost or moves to the pool of retrial customers. The service time is exponentially distributed with the rate dependent on the customer’s type. Such queueing system is suitable for modeling cognitive radio. Type-1 customers are interpreted as requests generated by primary users. Type-2 customers are generated by secondary or cognitive users. The problem of optimal choice of the threshold M is the subject of this paper. Behavior of the system is described by the multidimensional Markov chain. Its generator, ergodicity condition, and stationary distribution are given. The system performance measures are obtained. The numerical results show the effectiveness of considered admission control